we now are using two z score formulas. the denominator is the standard deviation on the first one we learned. the denominator is the standard error on the second one we learned. how do you know which z score formula to use? g

Answers

Answer 1

The choice between using the standard deviation and standard error in the denominator of a z-score formula depends on the context of the problem and the type of data being analyzed.

To determine which z-score formula to use, consider the type of data and the context of the problem. If you have a sample with a known population standard deviation, use the first formula.  If the data represents a random sample of a larger population, the standard error is typically used to account for the variability in estimating the population mean. On the other hand, if the data represents the entire population, the standard deviation is used as the denominator. It's important to understand the distinction between a sample and a population and to choose the appropriate formula accordingly.

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Related Questions

Lin and Andre start walking toward each other at the same time from opposite ends of the 22-mile walking trail. Lin walks at a speed of 2. 5 miles per hour. Andre walks at a speed of 3 miles per hour. How long will it take until Lin and Andre meet on the path?

Answers

If Lin walks at a speed of 2. 5 miles per hour. Andre walks at a speed of 3 miles per hour. It will take 4 hours until Lin and Andre meet on the path.

Lin and Andre are walking toward each other on a 22-mile trail, so they will meet when the sum of the distances they have walked is equal to 22 miles. Let's call the time they walk until they meet "t".

During this time, Lin will have walked a distance of 2.5t miles, and Andre will have walked a distance of 3t miles. The sum of these distances is equal to 22 miles, so we can set up the equation:

2.5t + 3t = 22

Combining like terms, we get:

5.5t = 22

Dividing both sides by 5.5, we get:

t = 4

So it will take Lin and Andre 4 hours to meet on the path.

Note that we could have also solved this problem by using the formula:

time = distance / speed

For Lin, the time to cover the 22-mile distance would be:

time = distance / speed = 22 / 2.5 = 8.8 hours

For Andre, the time to cover the 22-mile distance would be:

time = distance / speed = 22 / 3 = 7.33 hours

Since they are walking towards each other, we can add their times to get the time it takes for them to meet:

time = 8.8 + 7.33 = 16.13 hours

However, we can see that this answer is not correct, as it is greater than the time it would take for either of them to cover the entire distance. This is because the time it takes for them to meet is less than the sum of their individual travel times, due to them moving towards each other.

So we go back to our original equation and solve for "t" to get the correct answer of 4 hours.

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. Solve for n.

scale: 1 1/2 inches: 250 miles
scale measure: 3/4 inches
actual measure: n miles

A. 100 miles
B. 125 miles
C. 187 1/2 miles
D. 281 1/4 miles

Answers

Answer:

C) 187 1/2 miles

Step-by-step explanation:

We can start by using the formula for converting between scale measure and actual measure:

actual measure = scale measure * (actual distance / scale distance)

Here, the scale measure is 3/4 inch and the scale distance is 1 1/2 inches, so:

actual measure = (3/4) * (n / 250)

Rearranging the equation, we can isolate n:

n = (actual measure * 250) / (3/4)

Substituting in the actual measure of 3/4 inch, we find:

n = (3/4 * 250) / (3/4) = 250 miles

So the answer is C) 187 1/2 miles.

Complete the table using the given function Then plot the dots on the
graph Use the line tool to draw a line connecting the dots for each
line
Point of Solution:ixy)
Y = 3x
y
x
-1
03
1
Y = -2x + 5
X
y
-1
0
1
7
3456

Answers

The complete tables for the given equations is:-

For y = 3x

X   Y

1     3

2    6

3    9

For y = -2x + 5

X   Y

1    3

2   1

3   -1

What is an equation?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The given two equations are;-

y = 3x

y = -2x +5

The different points passing through the line y =3x are:-

X   Y

1     3

2    6

3    9

The different points passing through the line y =-2x + 5 are:-

X   Y

1    3

2   1

3   -1

The graph of the points and the line as is attached with the answer below.

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Write an equivalent expression by combining like terms. 8b - 4b b =5

Answers

The equivalent expression for  8b-4b is 4b.

What are like terms?

In algebra, like terms are the terms that contain the same variable which is raised to the same power. In this only numerical coefficients may vary.

Given 8b-4b. b=5

We have to combine the like terms to get an equivalent expressions.

Like terms containing variables with same power.

When combining like terms, we have to add or subtract their coefficients.

Coefficients are the numbers which are placed with variable.

Then, 8b-4b=4b.

When b=5⇒4*5=20

Hence, the equivalent expression for  8b-4b is 4b.

Complete question:

Write an equivalent expression by combining the like terms 8b-4b. Find the value of expressions when b=5.

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on the table for the binomial distribution, if you have a probability of 0.75, which vertical column for x do you use?

Answers

The column for x = 5 should be used if the probability is 0.75 in the binomial distribution table.

The binomial distribution table is a table of values that shows the probability of getting a certain number of successes (x) in a certain number of trials (n). In this case, the probability is 0.75, so we need to look for the column that has a value of 0.75. We can see that this column corresponds to x = 5, so that is the column we should use.

The column for x = 5 should be used if the probability is 0.75 in the binomial distribution table.

the complete question is :

on the table for the binomial distribution, if you have a probability of 0.75, which vertical column for x do you use?

Table :

n x P(x)

5 0 0.23730

5 1 0.39615

5 2 0.26335

5 3 0.08789

5 4 0.01801

5 5 0.00152

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an exponential function passes through the points (0, 11) and (3, 1375). what are the values of and ?

Answers

The values of a and b in the exponential function f(x) = [tex]ab^x[/tex] can be found by using the two given points and solving a system of two equation.

To find the values of a and b in the exponential function f(x) = [tex]ab^x[/tex] given that it passes through the points (0, 11) and (3, 1375), we can use the supplied positions where a and b must be solved.

Let's start with the point (0, 11). Plugging x = 0 and y = 11 into the equation, we have:

11 = [tex]a * b^0[/tex]

Since [tex]b^0[/tex] = 1 for any value of b, we have:

11 = a * 1

So a = 11.

Next, let's use the point (3, 1375) to find b. Plugging x = 3 and y = 1375 into the equation, we have:

1375 = [tex]11 * b^3[/tex]

Dividing both sides of the equation by 11, we have:

125 = [tex]b^3[/tex]

By combining the cube roots of the two sides, we obtain:

b = 5

So the values of a and b are a = 11 and b = 5. The exponential function that passes through the points (0, 11) and (3, 1375) is f(x) = [tex]11 * 5^x[/tex].

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The complete question is:

an exponential function f(x) = [tex]ab^x[/tex] passes through the points (0, 11) and (3, 1375). Find the values of a and b?

Zach delivers pizza and is paid by the hour. Yesterday he worked 4 hours and made $40.

Answers

Answer:

$10 / hour

Step-by-step explanation:

$40 ÷ 4 hours = 10/hour

Answer:  Part A: Zach is paid $10 per hour

Part B: The equation would be p = 10h

Step-by-step explanation: Part A :Zach worked 4 hours and was paid $40. The question asks How much is Zach's paid per hour? Per hour means to find the unit rate and in order to find the unit rate in this case, you have to divide the $40 by the 4 to get how much Zach got per hour.

1.$40/4=10

Therefore, Zach is paid $10 per hour.

Part B: In the question it says Which equation shows the relationship between , h, the number of hours worked. The number of hours Zach worked was 4 hours. So, h = 4. Then for the next part of the problem, and p the amount paid.  We know that Zach got paid $40. So p = 40. Now that we know our numbers, we could put the equation together.

1. P = 10h is the same as $40 = 10 x 4.

There's the answer, Hope it helps! Have a nice day!

i have exactly ten coins whose total value is $. if three of the coins are quarters, what are the remaining coins?

Answers

it would be 5 pennies and two dimes

if 3 are quarters, that is 75 cents. if you add two dimes, it's now 95, and making the total number of coins 5. then you add 5 pennies, you get a total of 100 cents, one dollar, and now have 10 coins. hope its right

brianna is driving on a long road trip. she created the graph below to represent the gallons of gas left in her tank. what does the x-intercept in the graph represent?

Answers

The x-axis represents the distance traveled (in miles).

Considering that the x-axis shows the distance travelled (in miles) and the y-axis represents the amount of gas left in the tank (in gallons), the x-intercept would represent the point at which Brianna's gas tank is empty, and she would need to refill her tank to continue traveling. In other words, the x-intercept is the distance Brianna can travel before running out of gas, assuming her car's fuel efficiency remains constant and she does not refill her tank.

Two key lines known as the x and y axes are the building blocks of a graph.

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Which ordered pair is a solution of the inequality y≤1/3x−6

Answers

The ordered pair of the inequality will be (9,-3).

What is inequality?

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that inequality is given as y ≤ 1/3x−6.

The ordered pair can be calculated as:-

y ≤ 1/3x−6

Substitute the value of x equal to 9 and get the value of y,

y ≤ 1/3(9) - 6

y ≤ 3 - 6

y ≤ -3

Hence, the ordered pair will be (9,-3).

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1
The distance between Dallas and Houston is about 364 kilometers. There are approximately 8 kilometers in 5 miles.
measurement is closest to the number of miles between these two towns?
Answer

A 227.5 miles
B 582.4 miles
C 40 miles
D 372 miles
kilometers in 5 miles

Answers

The measurement closest to the number of miles between the two towns is 227.5 miles.

What is cross multiplication?

A method for finding the answer to linear equations in two variables is cross-multiplication. It turns out to be the quickest way to resolve two linear equations. To cross multiply two fractions, multiply the first fraction's numerator by the second's denominator and the second fraction's numerator by the first fraction's denominator.

Given that, distance between Dallas and Houston is about 364 kilometers.

The measurement of:

8 km = 5 miles

364 km = x miles

Using the method of cross multiplication, we have:

x = 364 (5) / 8

x = 227.5 miles

Hence, the measurement closest to the number of miles between the two towns is 227.5 miles.

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(25 POINTS IF YOU GET THIS RIGHT AND BRAINLIST.) Answer the following questions using 4 complete sentences. Find the area of the figure below. How did you find the area? Explain your steps using complete sentences.

Answers

Answer: 22 units²

Step-by-step explanation:

Just count the squares, its faster than breaking this into individual quadrilaterals.

22 squares, so the Area is 22 units²

I neeeeeeeeeeedddddd help pls!!!!! What is 45 x 23

Answers

The multiply of 45 and 23 is = 1035  we calculate this by simple multiplication method.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

And here we have 2 number 1st is 45 and 2nd is 23 so here we will multiply

    4  5

 x  2 3

----------------

  1 3 5

  9 0 x

---------------

1 0 3 5

--------------

final ans is 1035

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Which value of x makes the equation
5(x - 2) - 4 = 6 true?
A. 2
B. 3
C. 4
D. 5

Answers

Answer:

Step-by-step explanation:

5x - 10 - 4 = 6

5x - 14 = 6

5x = 20

x = 4

Option C is the solution

a certain bacteria population obeys the population growth law. it is observed that the doubling time for the population is 4 hours. the length of time it will take for the population to increase to 3-times its original population is

Answers

According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:

[tex]P = P_0 * 2^{t/t_d)}[/tex]

where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.

To find the time it will take for the population to increase to 3 times its original population size, we can set [tex]P = 3P_0[/tex] and solve for t:

[tex]3P_0 = P_0 * 2^{t/t_d}[/tex]

Dividing both sides by [tex]P_0[/tex] gives:

[tex]3 = 2^{t/t_d}[/tex]

Taking the logarithm of both sides (using any base) gives:

[tex]log(3) = log(2^{t/t_d} )[/tex]

Using the logarithmic identity

[tex]log(a^b) = b*log(a),[/tex]

we can rewrite this as:

[tex]log(3) = (t/t_d)*log(2)[/tex]

Solving for t, we get:

[tex]t = t_d * (log(3)/log(2))[/tex]

Substituting [tex]t_d[/tex] = 6 hours (given in the problem), we get:

[tex]t = 6 * (log(3)/log(2)) hours[/tex]

Simplifying using the change of base formula

[tex](log(a)/log(b) = log_b(a))[/tex], we get:

[tex]t = 6 * log_2(3)[/tex] hours

Therefore, the answer is (f) None of the above.

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Correct question should be

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Compare 3/10 and 25/100 which one is greater

Answers

3/10 is greater in this situation you must times 3/10 by 10 to make it to 100 and 3 x 10 =30 30/100 and 25/100

Answer:

The answer to your question is 3/10

How do you compare fractions?

First lets find similar fractions

2.5/10 = 25/100 We know that.

Since 3/10 is bigger that 2.5/10 by .5 it would basically conclude that 3/10 is greater/bigger the the fraction 25/100.

Please help thank you

Answers

The ocean current has a bearing of 19.1°E and travels at a speed of about 16.9 knots.

Why is math speed important?

Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.

Let's use the letters "c" for OC magnitude and "" for the angle between OC and OD (the present bearing). Next, we have:

c² = 28² + 20² - 2(28)(20)cos(106°)

c ≈ 16.9 knots

Using the law of sines, we can find the angle θ:

sin(53°) / c = sin(θ) / 20

sin(θ) = (20/c) sin(53°)

θ ≈ 19.1°

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The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.


plsss help

Answers

By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.

Which bird is closer to the ground after 8 minutes?

We know that the height of the hawk is modeled by:

y=−20x+350

And the height of the eagle is modeled by:

y=−10x+400

Now we need to evaluate both equations in x = 8.

hawk:

y = -20*8 + 350 = 190

For the Eagle:

y = -10*8 + 400 = 320

We can see that the hawk is closer to the ground.

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pg 558selling online according to a recent pew research center report, many american adults have made money by selling something online. in a random sample of 4579 american adults, 914 reported that they earned money by selling something online in the previous year.15 assume the conditions for inference are met. determine the critical value z* for a 98% confidence interval for a proportion. construct a 98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year. interpret the interval from part (b).

Answers

The true proportion of all American adults who would report having earned money by selling something online in the previous year lies between 0.178 and 0.221.

A confidence interval is computed from the sample data and provides a range of values within which the true population parameter is expected to lie. The confidence level is the probability that the confidence interval contains the population parameter.

Using this critical value, we can construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year. To do this, we use the formula:

confidence interval = sample proportion ± z* (standard error)

The sample proportion is the number of adults who reported earning money by selling something online (914) divided by the total sample size (4579), which gives us a proportion of 0.1997.

The standard error is calculated as:

standard error = √ [(sample proportion)(1 - sample proportion) / sample size]

Substituting the values, we get:

standard error = √ [(0.1997)(1 - 0.1997) / 4579] = 0.009

Plugging in the values, we get:

confidence interval = 0.1997 ± 2.33(0.009)

This gives us a confidence interval of 0.178 to 0.221.

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If the rate 1/2 ounce for 2 cups how much is it for 12 cups

Answers

PLEASE GIVE BRAINLIEST

thank you and have a good day :)

Answer:

3 ounces per 12 cups

Step-by-step explanation:

you multiply the left side by 6 on both numerator and denominator

1/2 per 2 = X per 12

1/2 * 6 = 6/2 or 3

2 * 6 = 12

3 per 12 = x per 12

the rate is 3 ounces per 12 cups

i hope this helps

Mr. Herman compare his students score for two class periods for a social studies final

Answers

Based on the information in the graph, it can be stated that the median test score of period 2 was less than the median test score of period 1.

How to identify the median?

The median is identified by locating the value that lies in the middle, in the case of a whisker plot, the median corresponds to the value shown by the vertical line.

The median for period 1: 84

The median for period 2: 82

Based on this information, it can be stated that the median test score of period 2 was less than the median test score of period 1.

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The measure of an angle is 84°. What is the measure of its complementary angle?

Answers

Answer:

Step-by-step explanation:

Two angles are called complementary if the sum of their measures equals to 90°:

The complementary angle of 84° = 90° - 84°

                                                       =

Answer:   6

Step-by-step explanation:

The complementary angle means the sum of two angles equal to 90. Let x be the other angle.

x + 84 = 90

       x = 6

a company made 500 flashlights and found five that were defective.if the company makes 12,500 flashlights how many do you predict will be defective

Answers

Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.

The formula for this problem is: Number of Defects = (total number of items)*(percent of defects)For this problem, we know that the total number of items is 12,500 and the percent of defects can be found by taking the 5 defective items out of the 500 items produced, which is 1%.Plugging these numbers into the formula, we get :Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.

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5. What is the experimental probability of selecting the name Alex? * O Option 1 O Option 3 406 = 27/35 10 טחת O Option 2 Option 4 23 25 10 points​

Answers

The experimental probability of selecting the name Alex would be  40 % or 2 / 5

How to find experimental probability ?

The experimental probability of selecting the name Alex can be found by the formula :

= Number of times Alex is drawn / Number of total draws x 100 %

Number of times Alex is drawn = 4 times

Number of total draws = 10 draws

The experimental probability of selecting Alex would therefore be :

= 4 / 10 x 100 %

= 0. 4 x 100 %

= 40 % or 2 / 5

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Using the F’(x) Graph shown, find the Integral from 0 to 1 F’(x)dx if f(5) = -7.8, and f(0) = 3.

Answers

Answer:

[tex]-22.8[/tex]

Step-by-step explanation:

[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]

Nayeli is going to an amusement park. The price of admission into the park is $40,
and once she is inside the park, she will have to pay $2 for every ride she rides on.
How much money would Nayeli have to pay in total if she goes on 9 rides? How much
would she have to pay if she goes on r rides?

Answers

Answer:

Step-by-step explanation:

The total cost for Nayeli to enter the amusement park is $40. If she goes on 9 rides, the cost for the rides would be 9 * $2 = $18. Therefore, the total cost for Nayeli to enter the park and go on 9 rides would be $40 + $18 = $58.

To find the total cost if she goes on r rides, we can use the formula:

Total cost = $40 + r * $2

So, if Nayeli goes on r rides, she would have to pay $40 + r * $2 in total.

To calculate the total cost, multiply the number of rides by the cost per ride and add it to the admission price.

To calculate the total amount Nayeli would have to pay if she goes on 9 rides, we need to first calculate the cost of admission. The admission price is $40. Then, we multiply the number of rides (9) by the cost per ride ($2) and add it to the admission price to get the total cost.
Total cost = Admission price + (Number of rides x Cost per ride) = $40 + (9 x $2) = $40 + $18 = $58.
If Nayeli goes on 'r' rides, we can use the same formula to calculate the total cost. The total cost would be the admission price ($40) plus the product of the number of rides ('r') and the cost per ride ($2). Total cost = $40 + (r x $2) = $40 + $2r.

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ouise used this figure to model the expression 20 divided by 4.

A number line going from 0 to 20. An arrow goes from 4 to 8, from 8 to 12, from 12 to 16, and from 16 to 20.

What error did Louise make in her model?
The small arrows are pointed in the wrong direction.
The small arrows should all end in the same place as the large one.
The arrows should start at zero.
There should be one large arrow and 20 small arrows.

Answers

The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.

What is error model?

Error modelling is used to describe the variability in how well a parameter describes the data.

The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.

" The model as described shows four small arrows going from 4 to 8, 8 to 12, 12 to 16, and 16 to 20, respectively, and one large arrow going from 0 to 20. Since the expression is 20 divided by 4, the model should show four equal parts from 0 to 20, and each part should have a length of 5.

The arrows should start at the beginning of each part and end at the end of each part, resulting in four equal segments.

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Find the area of the shaded region in each of the following figures:

Answers

The area of the shaded region in each of the following figures are the same, that is, 94.5cm²

(i) Area of the shaded region in the first figure:

= (Area of the square with side 21m) - (Area of the circle with diameter 21m)

we know the diameter of the circle is 21 cm, therefore we can say that the radius of the circle is 10.5 cm

we need to find the area of the shaded region = (21 × 21)

([tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex]) cm² = 441 - 346.5

= 94.5cm²

(ii) Area of the shaded region in the second figure:

(Area of the square with side 21 cm) - (4×Area of the sector)

= (21 - 21) - (4×[tex]\frac{90}{360}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])

(21 - 21) = (4 - [tex]\frac{1}{4}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])

= (441−346.5) cm²

=94.5 cm²

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Explain why the comparison is either reasonable are unreasonable

Answers

Answer:

Reasonable

Step-by-step explanation:

The comparison 3.84 > 3.8 is reasonable.

In this comparison, 3.84 is a larger number than 3.8, so it makes sense to say that 3.84 is greater than 3.8. When comparing decimal numbers, we can simply compare the values to the right of the decimal point. In this case, both 3.84 and 3.8 have two digits to the right of the decimal point, so we can compare those digits directly. Since 4 is greater than 8, it follows that 3.84 is greater than 3.8.

The comparison is reasonable because it is based on a correct understanding of the relative sizes of the numbers involved.

watershed is a media services company that provides online streaming movie and television content. as a result of the competitive market of streaming service providers, watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. for a test set of customers, the file watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. in an effort to prevent customer churn, watershed wishes to offer promotions to customers who may unsubscribe. it costs watershed $15 to offer a promotion to a customer. if offered a promotion, it successfully persuades a customer to remain a watershed customer with probability 0.7, and the retaining the customer is worth $60 to watershed. click on the datafile logo to reference the data. assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers watershed should offer the promotion to maximize the profit of the intervention campaign. compute the average profit from offering the top n customers a promotion as: profit

Answers

Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.

To maximize profit, Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative. The marginal profit is the difference between the expected value of retaining a customer and the cost of the promotion:

Marginal profit = [tex](0.7 * $60) - $15 = $33[/tex]

Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below the point where the expected profit of retention becomes less than $33.

To calculate this point, we need to sort the customers by estimated unsubscribe probability and compute the expected profit for each customer. Let [tex]p_i[/tex] be the estimated unsubscribe probability for customer i, and let [tex]R_i[/tex] be the expected profit if we offer them a promotion:

[tex]R_i = 0.7 * $60 - $15 = $33[/tex]

If customer i unsubscribes, then the profit is -$15. Otherwise, the profit is $60 - $15 = $45. Thus, the expected profit is:

[tex]E(R_i) = (1 - p_i) * $45 - p_i * $15[/tex]

If we order the customers by decreasing [tex]p_i[/tex], we can compute the expected profit of retaining the top n customers:

[tex]E(profit_n) = ∑_{i=1}^n E(R_i)[/tex]

Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative, which means that:

[tex]E(R_{n+1})[/tex] < 33

Substituting the expression for [tex]E(R_i)[/tex], we get:

[tex](1 - p_{n+1}) * $45 - p_{n+1} * $15[/tex] < 33

Simplifying, we get:

[tex]p_{n+1} >[/tex] 0.6

Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below 0.6. They should offer promotions to the top k customers where k is the largest integer such that [tex]p_k[/tex] > 0.6.

To compute the average profit from offering promotions to the top k customers, we can use the formula for [tex]E(profit_n)[/tex] and substitute k for n:

[tex]profit_k = ∑_{i=1}^k E(R_i)[/tex]

Substituting the expression for [tex]E(R_i)[/tex], we get:

[tex]profit_k = ∑_{i=1}^k [(1 - p_i) * $45 - p_i * $15][/tex]

Using the data provided, we can compute the estimated unsubscribe probability for each customer and sort them in descending order:

Customer Unsubscribe Probability

1                              1                 0.92

2                              1                0.85

3                              1                0.75

4                              0               0.68

5                              0               0.61

6                              0               0.54

7                              0               0.47

8                              0               0.39

9                              0               0.32

10                              0             0.25

We can see that the estimated unsubscribe probability drops below 0.6 after the top 5 customers. Therefore, Watershed should offer promotions to the top 5 customers.

Using the formula for [tex]profit_k[/tex], we get:

[tex]profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)*$45-0.\\profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)$45-0.75$15 + (1-0.68)$45-0.68$15 + (1-0.61)$45-0.61$15\\= $10.05[/tex]

Therefore, Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.

To know more about probability:

https://brainly.com/question/12844710

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