A population of values has a normal distribution with μ=62.9 and σ=25.8. You intend to draw a random sample of size n=22.
Answers
In a population of values having a normal distribution with (μ = 62.9) and (σ = 25.8), and we intend to draw a random sample of size (n = 22),
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is 0.2476
(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is (0.0007)
As per the question statement, a population of values has a normal distribution with (μ = 62.9) and (σ = 25.8) and we intend to draw a random sample of size (n = 22).
We are required to calculate:
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3)
(ii) The probability that a sample of size (n = 242) is randomly selected less than 45.3 [P(M < 45.3)].
Let us assume that, a random variable "X" follows normal distribution with mean (μ = 62.9), standard deviation (σ = 25.8) and a sample size of (n = 22).
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is,
P (X < 45.3) = P[{(X - μ)/σ} < {(45.3 - 62.9)/25.8}]
= [P{Z < (-0.6822)}]
=0.247556247343...[Using Excel Function "NORMSDIST (-0.6822)]
≈ 0.2476
(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is,
P(M < 45.3) = P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/25.8/√22)}]
= P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/5.5006}]
=P[Z < (-3.19965)]
= (0.000687972836)...[Using Excel Function "NORMSDIST (-1.49)]
≈ 0.0007
Probability: Probability is the branch of mathematics concerning numerical descriptions about the extent to which an event is likely to occur, or how likely it is that, a proposition is true, and is measured by the ratio of the favorable cases to the whole number of cases possible.Sample: In statistics, quality assurance, and survey methodology, sampling is a logical selection of a subset (a statistical sample) of individuals from within a larger statistical population to estimate characteristics of the whole population.To learn more about Samples and Probability, click on the link below.
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Related Questions
Study Surface Area and Volume of Pyramid and Cone. How to find lateral area and total surface area of pyramid? please include one(1) problem per question with solutions.
Answers
Let's apply the formula for the lateral area and total surface area of a pyramid.
• Lateral Surface Area:
To find the lateral area of a pyramid, apply the formula:
[tex]A_l=\frac{1}{2}ps[/tex]Where:
p is the perimeter of the base
s is the slant height.
Example:
From the above square base pyramid, we have:
length of base, b = 4 cm
Slant height, s = 3 cm
Let's find the lateral area.
Since the base is a square, the perimeter will be:
p = 4 x 4 = 16 cm
Hence, to find the lateral area, we have:
[tex]\begin{gathered} A_l=\frac{1}{2}ps \\ \\ A_l=\frac{1}{2}\times16\times3 \\ \\ A_l=24\operatorname{cm}^2 \end{gathered}[/tex]Therefore, the lateral area of the square base pyramid above is 24 cm².
• Total surface area of a pyramid.
To find the total surface area of a pyramid, apply the formula:
[tex]A_s=\frac{1}{2}Ps+A[/tex]Where:
A is the area of the base
p is the perimeter of the base
s is the slant height.
Or we can simply say, the formula for total surface area is:
Total surface area = Lateral area + Area of base
Example:
Using the squarea base pyramid above, we have:
Area of base = 4 x 4 = 16 cm²
Lateral area = 24 cm²
Total surface area = 24 cm² + 16 cm² = 40 cm².
Which of the following represents a compound?
H
H-3
H2O
O-16
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Answer:
Step-by-step explanation:
A six-sided number cube is rolled, and then a spinner with five equal sections labeled A through E is spun. What is the probability of rolling a number less than four and spinning a D?
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Data:
• A six-sided number cube is rolled.
,• Then, a spinner with five equal sections labeled A through E is spun.
,• Probability of rolling a number less than four and spinning a D.
Procedure
To get the total probability, we have to get the probability for each situation.
• Six-sided number cube
As we have six sides, we have six numbers, then we can get the probability of rolling a number less than four, meaning rolling 3, 2 or 1, as follows:
[tex]P(x<4)=\frac{3}{6}=\frac{1}{2}[/tex]• Spinner with five equal sections
Similarly, we have five sides and we want to know the probability of getting a D:
[tex]P(x=D)=\frac{1}{5}[/tex]• Total probability
Finally, the total probability, as those are independent events, would be the multiplication of the probabilities:
[tex]P=\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}[/tex]Answer: 1/10
Answer:
1/10
Step-by-step explanation: I took the test
6. Which inequality has the solution set shown in the graph below? cont OTTO -7 -6 -5 -4 -3-2-1-1 1 2 3 4 5 6 7 T
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First we need write the equation of the line
we start from the general equation
[tex]y=mx+b[/tex]we need find m(slope) and b(cut point)
for the slope
we choose 2 points and find
(0,5)and(1,3)
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{3-5}{1-0} \\ m=-\frac{2}{1} \\ m=-2 \end{gathered}[/tex]the slope is -2
we can replace on the general equation with a point(0,5) and solve b
for b
[tex]\begin{gathered} y=(-2)x+b \\ 5=(-2)(0)+b \\ 5=0+b \\ b=5 \end{gathered}[/tex]replacing m and b, the final equation is
[tex]y=-2x+5[/tex]now, our inequality tells us that it takes into account the values below the line without taking the line (because it is dotted)
so we change = for <
the inequality is
[tex]y<-2x+5[/tex]
Select two values that are less than m.
+
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Answer:
A, D are correct.
Step-by-step explanation:
M=1.2 according to the image so anything below that is the answer.
Find the equation (in terms of x ) of the line through the points (-2,4) and (1,-5)y=
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To determine the equation of a line that passes through (x₁,y₁) you can use the following formula:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Substituting the given points in the above formula, you get:
[tex]y-4=\frac{4-(-5)}{-2-1}(x-(-2)).[/tex]Simplifying you get:
[tex]\begin{gathered} y-4=\frac{9}{-3}(x+2), \\ y-4=-3(x+2). \end{gathered}[/tex]Taking the above solution to its slope-intercept form, you get:
[tex]\begin{gathered} y=-3x-6+4, \\ y=-3x-2. \end{gathered}[/tex]Answer: [tex]y=-3x-2.[/tex]A recipe called for the ratio of sugar to flour to be 4:1 if you used 28 ounces of sugar how many ounces of flower would you need to use
Answers
Using ratios we can conclude that we need 7 ounces of flour.
What is the ratio?When the second number in the ordered pair, b, is not equal to 0, the ratio is written as a/b. An equation in which two ratios are made equal is known as a proportion. As an illustration, you could write the ratio as 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. The proportions of oranges to the total amount of fruit are 8:14 for oranges and 6:8 for lemons, respectively.So, ounces of flour need:
The ratio of sugar to flour is 4:1.The sugar used is 28 ounces.Then calculate for flour as follows:
4:1 = 28:x4/1 = 28/x4x = 28x = 28/4x = 7
Therefore, using ratios we can conclude that we need 7 ounces of flour.
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127x
10
0
6
4
--5-4-3 1₂
10
Mark this and return
169
909
4 5 6 x
Which statement is true regarding the functions on the
graph?
Of(-3)=g(-4)
Of(-4)= g(-3)
Of(-3)=g(-3)
Of(-4)= g(-4)
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Answer:
NJ and the other day and t I don't know what to do it again and again and again and again and again and again and again and again and again and again and again and again and again I will be a good night my dear sister and her and I will have to go in
which statements are true about points A,B, and C check all that applyA. the coordinates of point a are (3, -3)B. the coordinates of point B (1, -3)C. the coordinates of Point C are (-2,2)D. Point C is the closest to the Y axisE. points A and B are the same distance from the y-axisIk the pic is blurry sorry
Answers
By the graph, we can see that the only statement that apply is B. the coordinates of point B is (1, -3).
3x=8y-34y+2x=5Based on the system of equations above, what is the value of x/y?
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To solve the given system of equations, we can solve the first equation for x, then we combine the equations
[tex]\begin{gathered} 3x=8y-3 \\ x=\frac{8y-3}{3} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 4y+2x=5 \\ 4y+2(\frac{8y-3}{3})=5 \\ 4y+\frac{16y-6}{3}=5 \\ 4y+\frac{16}{3}y-2=5 \\ \frac{12y+16y}{3}=5+2 \\ \frac{28y}{3}=7 \\ 28y=7\cdot3 \\ y=\frac{21}{28} \\ y=\frac{3}{4} \end{gathered}[/tex]So, y = 21/28.
Now, we use the y-value to find x.
[tex]\begin{gathered} x=\frac{8\cdot\frac{21}{28}-3}{3}=\frac{\frac{168}{28}-3}{3}=\frac{\frac{84}{14}-3}{3}=\frac{\frac{42}{7}-3}{3} \\ x=\frac{\frac{42-21}{7}}{3}=\frac{\frac{21}{7}}{3}=\frac{3}{3}=1 \end{gathered}[/tex]Hence, the value of each variable is x = 1 and y = 3/4.if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<17
Answers
Since angle 16 measures 139 degrees and is a supplementary angle with angle 17, we have the following equation:
[tex]139+\measuredangle17=180[/tex]solving for angle 17, we get:
[tex]\begin{gathered} 139+\measuredangle17=180 \\ \Rightarrow\measuredangle17=180-139=41 \\ \measuredangle17=41\degree \end{gathered}[/tex]therefore, the measure of angle 17 is 41 degrees
Explain the meaning of the point (1,2.5) In terms of the situation
Answers
Given
The recipe for the smoothie is made up of 5 cups of strawberries and 2 cups of bananas.
For the point (1,2.5)
It means that from the graph showing a plot of the numbers of cups, with the number of strawberries cups on the y-axis and the number of banana cups on the x-axis, the 2.5 is for the number of cups for strawberries while 1 is the number of cups of banana.
We can also say that
For every 1 cup of banana, there should be 2.5 cups of strawberries.
1.64÷3??? -------------------
Answers
Answer:
0.54666666666
Step-by-step explanation:
i don't know why but that is the answer
Simplify.
[3 (4-2)] x (16-4x3)
O 10
O 24
O 360
O 468
Answers
hope that help s you soooooooooooooooooo much
write a function to describe the following scenario.a basketball player practices jump shots. she starts at zero points and scores 5 points per minute. how many points will she have scored after a certain number of minutes?Y = ?x
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number of minutes : x
number of points scored after x minutes : y
points scored per minute : 5
y=5x
multiply the points scored per minute (5) by the number of minutes (x). The expression is equal to the total number of points scored (y).
Using compatible numbers to estimate, which expression has a quotient of about 70?
O A. 3,424 ÷ 49
OB. 5,358 ÷ 89
O C. 6,409 ÷ 79
O D. 5,238 ÷ 89
Answers
A student must have an average (the mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of B. Devon’s grades on the first four tests were 76%, 65%, 89%, and 80%. What range of grades on the fifth test would him a B in the course? ( Assume that 100% is the highest grade possible.)
Enter the range of grades necessary for Devon to earn a b average.
__% < x < 100%
- -
Answers
Answer:
90% ≤ x ≤ 100%Step-by-step explanation:
Test results are:
76, 65, 89, 80 and x.The average of 5 tests should be:
80 ≤ average < 90, to get a B.The average is:
(76 + 65 + 89 + 80 + x)/5 = (310 + x)/5Plug it into inequality:
80 ≤ (310 + x)/5 < 90 Multiply by 5400 ≤ 310 + x < 450 Subtract 31090 ≤ x < 140But the maximum possible result from one test is 100%, considering this top score Devon must get:
90% ≤ x ≤ 100%need help with this problem drop down 1, 2 dashed, soliddrop down 3 4 below, above
Answers
The boundary line is graphed as a dashed line if the symbols < or > are used, and as a solid line if the symbols ≥ or ≤ are used.
For an inequality in slope-intercept form, the half-plane above the line is shaded if the symbols > or ≥ are used, and the half-plane or ≤ are used. the line is shaded if the symbols < or ≤ are used.
Complete each proof using the properties of equality. ALL POWS W
Type the properties how they are listed above.
18; Prove: = 10
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Ensuring that each person has an equal chance to maximize their potential is what equality is all about.
How is the equality property demonstrated?Proof: Given that A = B and B = C, we can infer that A = C according to the transitive principle. A = C and C = D are both true if we also know that C = D. We shall ultimately get at A = D after one more transitive property application.
The symmetrical attribute of equality
This fact, which states that if
18 + 10 =28,
then
28 = 10 + 18,
Serves as an example of the equality's symmetric property. The symmetric property of equality in mathematics is actually fairly straightforward. According to this principle, if a = b, then b =a.
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Solve the equation:2.5t=20
Answers
In order to solve this equation for t, we just need to divide both sides of the equation by 2.5.
So we have that:
[tex]\begin{gathered} 2.5t=20 \\ \frac{2.5t}{2.5}=\frac{20}{2.5} \\ t=\frac{20}{2.5} \\ t=8 \end{gathered}[/tex]So the solution for this equation is t = 8.
The Morgans bought a $333,000 condominium. They made a down payment of $47,000 and took out a mortgage for the rest. Over the course of 30 years theymade monthly payments of $1714.72 on their mortgage until it was paid off.(a)(b)What was the total amount they ended up paying for the condominium(including the down payment and monthly payments)?$1]How much interest did they pay on the mortgage?I need help with this math problem.
Answers
Given: The following on the purchase of a Condominium
[tex]\begin{gathered} Price(Condominium)=333000 \\ Down-payment=47000 \\ Monthly-payment=1714.72 \\ Time=30years \end{gathered}[/tex]To Determine: The total amount they ended up paying for the condominium
Solution
Please note that we have 12 months in a year. The total number of months in 30 years would be
[tex]\begin{gathered} 1year=12months \\ 30years=30\times12months \\ 3oyears=360months \end{gathered}[/tex]Total monthly payments would be
[tex]\begin{gathered} 1month=1714.72 \\ 360months=360\times1714.72=617299.20 \end{gathered}[/tex]Therefore, the total amount they ended up paying for the condominium would be the addition of the down payment and the monthly payments
[tex]Total-amount(Paid)=47000+617299.20=664299.20[/tex]Hence, the total amount they ended paying for the condominium is $664,299.20
The interest paid on the mortgage would be the difference between the total amount paid and the cost
[tex]\begin{gathered} Interest=(Total-amount-paid)-Cost(condominium) \\ =664299.2-333000 \\ =331299.20 \end{gathered}[/tex]Hence, the interest paid on the Mortgage is $331,299.20
y= -5x+2 (Function rule)
Answers
The complete table using function rule y = -5x+2 is:
x y
-2 12
0 2
2 -8
4 -18
What is a function rule for a table?A function table includes a function rule as well as input and output values. If we plug in various values for the input, we obtain corresponding values of output according to the function rule. The relationship between the input values x and the output values y always follows a pattern that is specified by the function rule.Given:
Function rule, y = -5x+2.
We have to find the values of y by substituting different values of x.
When,
x = -2
y = -5(-2) + 2 = 10+2 = 12
x = 0
y = -5(0) + 2 = 0+2 = 2
x = 2
y = -5(2) + 2 = -10+2 = -8
x = 4
y = -5(4) + 2 = -20+2 = -18
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Brainliest. Find x and length
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Value of x is 4 and length of QR is 15cm.
Define parallelograms.A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal. The illustration displays a parallelogram ABCD with the coordinates AB II CD and AD II BC. Moreover, AB = CD and AD = BC. Non-Example: A parallelogram is not represented by a trapezium.
Given Data
In rectangle, two parallel line are equal.
PS = -1+ 4x
QR = 3x +3
So,
Value of x will be:
-1 + 4x = 3x +3
4x - 3x = 3 +1
x = 4
For length of QR,
3x +3
3(4) +3
12 +3
15
Value of x is 4 and length of QR is 15cm.
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Find the value of w and YZ if Y is between X and Z
Answers
w = 4 and YZ=24
1) XY = 4w
YZ= 6w
XZ=12w-8
2) Let's draw this to better understand it
So using the Segment Addition Postulate principle, let's write and solve
12w-8 =4w+6w
12w-8=10w
12w-10w -8=10w-10w
2w-8=0
2w-8+8=8
2w=8
w=4
3) The value for YZ =
6w => 6(4) YZ =24
Most television show juice 13 minute of every hour for commercial leaving the remaining 47 minutes for the actual actual one popular television show wants to change the ratio of commercial time to show time to be 3 to 7 create two ratio tables one for normal ratio of commercials to programming and another one for the proposal ratio of commercial some programming use a ratio table to make a statement about which ratio with me and fewer commercials for viewers watch into our television
Answers
Answer: 39
Step-by-step explanation: 1889 - 1927 = 30
How do I plot this linear inequalitie
Answers
Given the following inequality:
[tex]y\ge x-4[/tex]To plot the inequality, first we will plot the line y = x - 4
We will graph the line using the intercepts
When x = 0, y = -4
When y = 0, x = 4
So, the line passes through the points (4, 0) and (0, -4)
The graph of the line will be solid
Now, we will find the area that will be shaded to represent the answer.
Use the point (0, 0)
So, 0 ≥ 0 - 4
So, the point (0, 0) lying in the solution area.
the plot of the inequality will be as shown in the following figure:
When x = 0, y = -4
When y = 0, x = 4
So, the line passes through the points (ng the intercepts
When x = 0, y =
help me please
thank you
Answers
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)
Vertex:
(−3, −11);
point:
(0, 7)
Answers
The standard form of the quadratic function is- y = 2x² + 12x + 7
Here, we are given-
Vertex coordinate = (-3, -11)
Point on the graph = (0, 7)
The vertex form of a quadratic equation is given as-
y = a(x - h)² + k
Where h, k are the coordinates of the vertex.
a is the letter in general form of quadratic equation which is-
y = ax² + bx + c
Thus, here, h = -3, k = -11, x = 0 and y = 7
Substituting these values in the vertex form we get-
7 = a(0 - (-3))² - 11
⇒ 7 + 11 = 9a
9a = 18
a = 18/9
a = 2
Thus, the standard form of the quadratic equation can be calculated as-
y = 2(x - (-3))² - 11
y = 2x² + 12x + 18 - 11
y = 2x² + 12x + 7
Thus, the standard form of the quadratic function is- y = 2x² + 12x + 7
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Adrian's favorite hobby is to take underwater pictures of his favorite sea creatures. Adrian decides to dive 48 feet below sea level so he can take pictures of seahorses that are 55 feet below sea level. What is the total distance
between him and the seahorses?
Answers
The total distance between Adrian and the seahorses is 7 feet.
How to calculate distance between two planes below sea level?
Since, the values of distances of the planes from the sea level are given as reference, mere linear subtraction of the smaller value from the larger value will bring in the distance between the seahorses and Adrian constructively; if the value turns out to be negative for unforeseen reasons, the modulus of the value obtained will serve the purpose.
Given, the distance from sea level where seahorses dwell = d₁ = 55 feet
The distance from sea level Adrian would dive = d₂ = 48 feet
Distance between seahorses and Adrian = d₁ - d₂ = (55 - 48) feet = 7 feet
Thus, the total distance between Adrian and the seahorses is 7 feet.
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escribe dos raciones q sean igual y explicalas
Answers
EXPLICACION.
Dos razones forman una proporcion cuando se da la siguiente condicion ;
el producto de sus extremos es igual al producto de sus medios.Veamos un ejemplo:
Un ejemplo de razones que se pueden hallar facilmente y saber si realmente es verdadera o exacta la proporcion es el siguiente ejemplo:
[tex]\begin{gathered} \frac{80}{4}=\frac{200}{10},\text{aqui debemos multiplicar en cruz} \\ entonces\text{ quedaria:} \\ 80\times10=200\times4 \\ \textcolor{#FF7968}{800=800;}\text{ } \\ \text{Como vemos el resultado es el mismo por lo tanto las dos razones } \\ \text{son iguales o verdadera.} \end{gathered}[/tex]