You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. This means that
(a) in every 100 bridge deals, each player has one ace exactly 11 times.
(b) in one million bridge deals, the number of deals on which each player has one ace will be exactly 110,000.
(c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%.
(d) in a very large number of bridge deals, the average number of aces in a hand will be very close to 0.11.
(e) None of these

The loan you can take is : Solid Savings & Loan at 9% interest for 4 years.

To determine which loan you can take, you need to calculate the monthly payments for each option.

For the loan from Solid Savings & Loan, the total interest over 4 years would be $3,600 ($10,000 x 0.09 x 4). This means that the total amount you would need to repay over 4 years would be $13,600 ($10,000 + $3,600). Divided by 48 months, your monthly payment would be $283.33 ($13,600 / 48).

For the loan from Fifth Federal Bank & Trust, the total interest over 3 years would be $2,100 ($10,000 x 0.07 x 3). This means that the total amount you would need to repay over 3 years would be $12,100 ($10,000 + $2,100). Divided by 36 months, your monthly payment would be $336.11 ($12,100 / 36).

Since you can afford to pay $250 per month, you cannot take the loan from Fifth Federal Bank & Trust as the monthly payment is higher than what you can afford. However, you can take the loan from Solid Savings & Loan as the monthly payment is $250. Therefore, the loan you can take is from Solid Savings & Loan at 9% interest for 4 years.

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The probability of one success is 0.203625 or 20. 4 %.

The probability that there is one success in a binomial probability which has a chance of success of 5 % can be found by the formula :

P ( X = 1) = (5 choose 1) x ( 0.05 ) x  (0.95 ) ⁴

= ( 0.05 ) x  ( 0. 95 ) ⁴

= 0.05 x 0.8145

= 0.040725

Multiplying both gives:

P(X = 1) = 5 x 0.040725

= 0.203625

In conclusion, the probability of one success is 0.203625 or 20. 4 %.

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Answer:

To create a matrix for this linear system, we can arrange the coefficients of the variables and the constants into a matrix as follows:

| 1 3 2 | | x | | 26 |

| 1 -3 4 | x | y | = | 2 |

| 2 1 1 | | z | | 8 |

To solve the system using row reduction, we can perform elementary row operations to transform the matrix into row echelon form or reduced row echelon form. I will use the latter approach for simplicity:

| 1 0 0 | | x | | 6 |

| 0 1 0 | x | y | = | 5 |

| 0 0 1 | | z | | -1 |

Therefore, the solution to the system is x = 6, y = 5, and z = -1.

a) The quadratic equation x² + 7x + 10 = 0 has two distinct real roots
b) The quadratic equation 4x² - 3x + 4 = 0 has two complex (non-real) roots.

The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by the expression b² - 4ac. The value of the discriminant can help us determine the nature of the roots of the quadratic equation.

Specifically:

If the discriminant is positive, then the quadratic equation has two distinct real roots.

If the discriminant is zero, then the quadratic equation has one real root (also known as a double root or a repeated root).

If the discriminant is negative, then the quadratic equation has two complex (non-real) roots.

Using this information, we can determine the number of real solutions for each of the given quadratic equations without actually solving them:\

a) x² + 7x + 10 = 0

Here, a = 1, b = 7, and c = 10.

Therefore, the discriminant is:

b² - 4ac = 7² - 4(1)(10) = 49 - 40 = 9

Since the discriminant is positive, this quadratic equation has two distinct real roots.

b) 4x² - 3x + 4 = 0

Here, a = 4, b = -3, and c = 4.

Therefore, the discriminant is:

b² - 4ac = (-3)² - 4(4)(4) = 9 - 64 = -55

Since the discriminant is negative, this quadratic equation has two complex (non-real) roots.

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There are 64 functions from set A to set B.

To determine how many functions there are from A = {1, 2, 3} to B = {a, b, c, d}, you can use the following step-by-step explanation:

1. Understand that a function maps each element of set A to exactly one element in set B.
2. Notice that set A has 3 elements, and set B has 4 elements.
3. For each element in set A, there are 4 choices in set B it can be mapped to.
4. Therefore, the total number of functions is equal to the product of the number of choices for each element in set A, which is 4 × 4 × 4 = 64.

So, there are 64 functions from A = {1, 2, 3} to B = {a, b, c, d}.

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Answer:

B) 6

Step-by-step explanation:

Firstly, we need to know what the question is asking for.

"How many miles does she need to run each hour to complete the run" is asking for a speed in miles per hour.

miles / hour = speed in mph

18 miles / 3 hours = 18/3 mph

18/3 simplifies to 6

Lisa needs to run 6 mph

The possible values of the coefficient (a) and an exponent (b) are CThe missing coefficient (a) can be any multiple of 3. The missing exponent (b) must be 5.

The two monomials are given as

ax³ 6xᵇ

Such that we have the LCM to be

LCM = 18x⁵

Since the coefficient of the LCM is 18, then the following is possible

a * 6 = multiples of 18

Divide both sides by 6

a = multiples of 3

Next, we have

LCM of x³ * xᵇ = x⁵

So, we have

b = 5 (bigger exponent)

Hence, the true statement is (c)

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We can state the critical values for the rejection rule as follows:

test statistic ≤ -1.645 (left-tailed test)

test statistic ≥ 1.645 (right-tailed test)

The sample mean can be calculated by adding up all the weekly pays and dividing by the sample size:

sample mean = (687.73 + 543.15 + ... + 703.06) / 50 = 638.55 (rounded to two decimal places)

To test whether the average weekly earnings for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma, we can perform a two-sample t-test assuming equal variances. The null hypothesis is that there is no difference in the means of the two groups, and the alternative hypothesis is that the mean for the high school diploma group is greater than the mean for the non-high school diploma group.

Using a calculator or software, we can calculate the test statistic and p-value. Assuming a two-tailed test and a significance level of 0.05, the critical values for the rejection rule are -1.96 and 1.96.

test statistic = 3.196 (rounded to three decimal places)

p-value = 0.0012 (rounded to four decimal places)

Since the p-value (0.0012) is less than the significance level (0.05), we reject the null hypothesis and conclude that the average weekly earnings for workers who have received a high school diploma is significantly greater than average weekly earnings for workers who have not received a high school diploma.

For a one-tailed test with α = 0.05, the critical value would be 1.645. The rejection rule would be: if the test statistic is greater than 1.645, reject the null hypothesis. Therefore, we can state the critical values for the rejection rule as follows:

test statistic ≤ -1.645 (left-tailed test)

test statistic ≥ 1.645 (right-tailed test)

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Answer:

The answer to your problem is, [tex]7\frac{1}{9}[/tex]

Step-by-step explanation:

Calculation process:

= [tex]\frac{16}{3}[/tex] ÷ [tex]\frac{3}{4}[/tex]

= [tex]\frac{16}{3}[/tex] × [tex]\frac{4}{3}[/tex]

= [tex]\frac{16*4}{3*3}[/tex]

= [tex]\frac{64}{9}[/tex] = [tex]7\frac{1}{9}[/tex]

Thus the answer to your problem is, [tex]7\frac{1}{9}[/tex]

Ben's final cost after the 15% discount will be $40.375

From the question, we have the following parameters that can be used in our computation:

Discount = 15%

Total purchase = $47.50

Using the above as a guide, we have the following:

Final cost = Total purchase * (1 -Discount)

Substitute the known values in the above equation, so, we have the following representation

Final cost = 47.50 * (1 -15%)

Evaluate

Final cost = 40.375

Hence, the final cost is $40.375

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If you invest $2,000 for 3 years at an interest rate of 6%, compounded every 6 months. The value of your investment at the end of the period is $2,397.39.

The interest rate is 6% and it is compounded every 6 months, so the period is 6 months. To calculate the value of the investment at the end of the period, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount.
P = the principal amount (initial investment)
r = the annual interest rate (6%).
n = the number of times the interest is compounded per year (2, since it's compounded every 6 months).
t = the time period in years (3)

Plugging in the numbers, we get:

A = 2,000(1 + 0.06/2)^(2*3)
A = 2,000(1 + 0.03)^6
A = 2,000(1.03)^6
A = $2,397.39

Therefore, the value of your investment at the end of the period is $2,397.39.

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The statement is true, if u > x and v > y then ged(u, v) > ged(x,y).

First, let's define ged(u,v) as the greatest common divisor of u and v.

Assuming that u > x and v > y, we can express u and v as:

u = x + m
v = y + n

where m and n are positive natural numbers.

Now, let's assume that ged(x,y) = d, where d is a positive natural number that divides both x and y.

Therefore, we can express x and y as:

x = dp
y = dq

where p and q are positive natural numbers.

Now, we can express u and v in terms of d as well:

u = dp + m
v = dq + n

Since m and n are positive natural numbers, it follows that ged(u,v) is a positive natural number as well.

Now, we need to show that ged(u,v) > d.

Assume the contrary, i.e. ged(u,v) ≤ d.

This means that there exists a positive natural number k that divides both u and v, and k ≤ d.

Since k divides both u and v, it must also divide their difference:

u - v = (d * p + m) - (d * q + n) = d * (p - q) + (m - n)

Therefore, k must also divide (m - n).

But since m and n are positive natural numbers, we have:

|m - n| < max(m,n) ≤ max(u,v)

Therefore, k cannot divide both (m - n) and max(u,v), which contradicts the assumption that k divides both u and v.

Therefore, our initial assumption that ged(u,v) ≤ d must be false, which means that ged(u,v) > d.

Therefore, the statement is true.

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Answer: Taylor will run out of money first after 9 months, while Danny will run out of money after 8 months.

Step-by-step explanation:

To solve this problem, we can set up two equations to represent Taylor and Danny's savings over time, where x is the number of months that have passed:

Taylor: 900 - 100x

Danny: 1200 - 150x

To find out when they have the same amount of money in their accounts, we can set the two equations equal to each other and solve for x:

900 - 100x = 1200 - 150x

50x = 300

x = 6

Therefore, Taylor and Danny will have the same amount of money in their accounts after 6 months. To find out how much money they will have at that time, we can substitute x = 6 into either equation:

Taylor: 900 - 100(6) = 300

Danny: 1200 - 150(6) = 300

So after 6 months, both Taylor and Danny will have $300 in their accounts.

To determine who runs out of money first, we can set each equation equal to zero and solve for x:

Taylor: 900 - 100x = 0

x = 9

Danny: 1200 - 150x = 0

x = 8

Therefore, Taylor will run out of money first after 9 months, while Danny will run out of money after 8 months.

Check the picture below.

so the horizontal lines are 4 and 12, and then we have a couple of slanted ones, say with a length of "c" each

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{4}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ c=\sqrt{ 4^2 + 3^2}\implies c=\sqrt{ 16 + 9 } \implies c=\sqrt{ 25 }\implies c=5 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{4+12+5+5}\implies \text{\LARGE 26}[/tex]

The statement that is true about the 2 functions, in which the relationship between the x and y-values in the table of values for both functions is a linear relationship is that The y-intercept of the graph of A is equal to the y-intercept of the graph of B

The equation representing the relationship in function A in point-slope form is therefore;

y - 12 = 6·(x - 2)

y - 12 = 6·x - 12

y = 6·x - 12 + 12 = 6·x

The equation in slope-intercept form, y = m·x + c, where c is the y-intercept is therefore; y = 6·x

The true statement is therefore; The y-intercept of the graph of A is less than the y-intercept of the graph of B

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The circle intersects the x-axis at the points (-5, 0) and (5, 0).

We have,

Using the Pythagorean theorem to find the radius of the circle.

So,

r = √(0-3)² + (0-4)²

r = √(9+16)

  = √25

  = 5

The equation of the circle is x² + y² = 5² = 25.

To find the points where the circle intersects the x-axis,

We substitute y = 0 in the equation of the circle and solve for x:

x² + 0² = 25

x² = 25

x = ±5

Therefore,

The circle intersects the x-axis at the points (-5, 0) and (5, 0).

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The value of c2 in the notation of the text is 4mk. The units of c2 are Ns/m.
To find the position of the mass after t seconds, we need to solve the differential equation:
m d^2x/dt^2 + c dx/dt + kx = 0
where m is the mass of the spring, c is the damping constant, k is the spring constant, and x is the position of the mass.
We can write the solution to this equation in the general form:
x(t) = G1eat cos( Bt) + ce" sin(St)
where a and B are constants that depend on the initial conditions of the system, and G1 and c are constants determined by those initial conditions.
To find the constants G1 and c, we need to use the initial conditions given in the problem: the spring is stretched 0.5 meters beyond its natural length and then released with zero velocity. This means that x(0) = 0.5 and dx/dt(0) = 0.

Substituting these initial conditions into the general solution, we get:
x(t) = G1e^(-ct/2m) cos( ωt) + c e^(-ct/2m) sin( ωt)
where ω = sqrt(k/m - c^2/4m^2) is the angular frequency of the motion.
To find the constants G1 and c, we differentiate x(t) with respect to time and use the initial condition dx/dt(0) = 0:
dx/dt = -G1c/2m e^(-ct/2m) sin( ωt) + c e^(-ct/2m) cos( ωt)
dx/dt(0) = 0 = c
Therefore, c = 0.
To find G1, we use the initial condition x(0) = 0.5:
x(0) = G1 cos(0) + 0 = G1 = 0.5
Therefore, the position of the mass after t seconds is:
x(t) = 0.5e^(-ct/2m) cos( ωt)
where c = 0 and ω = sqrt(k/m).
Plugging in the given values, we get:
x(t) = 0.5e^(-0t/2*7) cos( sqrt(40/7)t) = 0.5cos(2.226t)
So the position of the mass after t seconds is 0.5cos(2.226t) meters.

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The equation of the parabola is given as follows:

y = -28/19600(x - 140)² + 28.

The distances from the center for a height of 13 meters are given as follows:

37.53 m and 242.47 m.

The equation of a parabola of vertex (h,k) is given by the equation presented as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

It has a span of 280 meters, hence the x-coordinate of the vertex is given as follows:

x = 280/2

x = 140 -> h = 140.

The maximum height is of 28 meters, hence the y-coordinate of the vertex is given as follows:

y = 28 -> k = 28.

Hence the equation is:

y = a(x - 140)² + 28.

When x = 0, y = 0, hence the leading coefficient a is obtained as follows:

19600a = -28

a = -28/19600

Hence:

y = -28/19600(x - 140)² + 28.

The distance from the center at which the height is 13 meters is obtained as follows:

13 = -28/19600(x - 140)² + 28.

28/19600(x - 140)² = 15

(x - 140)² = 15 x 19600/28

(x - 140)² = 10500.

Hence the distances are obtained as follows:

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Answer: What is the question?

Step-by-step explanation:

Brainliest pls:)

X = $50,900 + (1.645 * $4,500)
X = $50,900 + $7,402.50
X ≈ $58,302.50
So, at a 95% confidence interval all students at private universities pays less than approximately $58,303.

To answer this question, we need to use the normal distribution formula:
z = (x - μ) / σ
where:
X = cost at the desired percentile
μ = mean annual cost ($50,900)
Z = z-score corresponding to the desired percentile (we'll find this value)
σ = standard deviation ($4,500)

where z is the z-score, x is the value we want to find, μ is the mean, and σ is the standard deviation.

In this case, we want to find the value of x such that 95% of all students pay less than that amount. We can find the corresponding z-score using a standard normal distribution table, which tells us the area under the curve to the left of a certain z-score. Since we want to find the value that corresponds to the 95th percentile, we look for the z-score that gives us an area of 0.95 to the left.

Using a standard normal distribution table, we find that the z-score for the 95th percentile is 1.645.

Now we can plug in the values we know:

1.645 = (x - 50,900) / 4,500

Solving for x, we get:

x = 58,427

So 95% of all students at private universities pay less than $58,427.
This is because we want to keep as much precision as possible until the final step, to avoid any rounding errors.

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a) The probability that X is within three standard deviations of the mean is approximately 1.

b) the probability that the drone will land out of the targeted area exactly 4 times is 0.00052.

c) The probability that the drone will land out of the targeted area at most 4 times is 0.1029

d) The expected value of X is 9.6.

e) The meaning of the expected value in the context of the story is average landing performance of the drone based on the given probability of success.

f) The variance of X is 0.7319.

g) The probability that it missed the target at most 2 times is 3.121.

h) The probability that it missed the target at least 2 times is 0.7319.

I) The probability that X is within three standard deviations of the mean is 1.3856.

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials with a constant probability of success.

The characteristics of a binomial random variable include the number of trials (n), the probability of success (p), the number of successes (x), and the mean and variance of the distribution.

Here we have

Binomial distribution We are testing the landing performance of a new automated drone. The drone lands on the targeted area 80% of the time. We test the drone 12 times.

a. X is a binomial random variable because we have a fixed number of independent trials and each landing has only two possible outcomes (landing on the targeted area or landing outside of it) with a constant probability of success (0.8).

The characteristics of the binomial distribution are:

The number of trials is fixed (n=12)

Each trial has only two possible outcomes (success or failure)

The probability of success (p) is constant for each trial

The trials are independent of each other

b. P(X = 4) = (12 choose 4) × (0.8)⁴ × (0.2)⁸ = 0.00052

c. P(X< = 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= 0.0687 + 0.2060 + 0.3020 + 0.2670 + 0.1854 = 0.1029

d. E(X) = np = 120.8 = 9.6

e. The expected value of X represents the average number of successful landings (in the targeted area) we would expect to see in a sample of 12 landings.

In the context of the story, it tells us the average landing performance of the drone based on the given probability of success.

f. Var(X) = np(1-p) = 120.80.2 = 1.92

g. P(X<=2 | X<=4) = P(X<=2)/P(X<=4)

= (P(X=0) + P(X=1) + P(X=2))/(P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4))

= 0.3217/0.1029 = 3.121

h. P(X>=2 | X<=4) = 1 - P(X<2 | X<=4) = 1 - P(X<=1 | X<=4) = 1 - (P(X=0) + P(X=1))/(P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)) = 1 - 0.2747/0.1029 = 0.7319

i. The standard deviation of a binomial distribution is √(np(1-p)). So, the standard deviation of X is √(120.80.2) = 1.3856. Three standard deviations above and below the mean would be 3*1.3856 = 4.1568.

Therefore,

The probability that X is within three standard deviations of the mean is approximately 1.

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There was a significant reduction in peoples over estimation of the line length, t = XXX with df = XXX, p < 0.01 two-tailed, with M = 10%, n = 25, s = 15%, Cohen's d = XXX , M = 10%, 95% CI [XXX, XXX].

8a. A. was
8b. B. t = XXX with df = XXX
8c. A. < 0.01 two-tailed
8d. C. M = 10%, n = 25, s = 15%, Cohen's d = XXX , M = 10%, 95% CI [XXX, XXX].

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The population of Pennsylvania is: 1304503 people

Population density is calculated by taking the total area of a region in question and dividing it by the total number of people that live in that area. The result will give the average number of inhabitants per square kilometre, mile, acre, meter, etc.

The parameters given are:

Population of colorado = 5,770,000 people

Area of colorado = 280 * 380

= 106,400 mi²

Population density here = 5,770,000/106,400

54.23 people per mi²

Area of Pennsylvania = 283 * 170

= 48110 mi²

Thus:

Population of Pennsylvania/48110 mi² = 5 * 54.23 people per mi²

Population of Pennsylvania = 48110 * mi² * 5 * 54.23 people per mi²

= 1304503 people

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The equation of the plane passing through point P with normal vector 2i + 6j + 7k is x + 3y + 4z = 48.

A: True.

The equation of a plane in 3D space is given by Ax + By + Cz = D, where A, B, C are the components of the normal vector and D is the distance from the origin to the plane along the direction of the normal vector.

In this case, the normal vector is 2i + 6j + 7k, so A = 2, B = 6, and C = 7. To find D, we can substitute the coordinates of the given point P into the equation of the plane:

2(1) + 6(3) + 7(4) = D

2 + 18 + 28 = D

D = 48

Therefore, the equation of the plane passing through point P with normal vector 2i + 6j + 7k is x + 3y + 4z = 48.

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Answer:

Its the first one

Step-by-step explanation:

correct answer

Answer:

The answer is m = 2 .

Step-by-step explanation:

14 - 3m = 4m

14 = 4m + 3m

14 = 7m

14/7 = m

2 = m

m = 2

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The surface area of the triangular base prism is 174 ft².

The prism above is a triangular prism. Therefore, let's find the surface area of the triangular prism as follows:

The prism has two triangular faces and three rectangular faces.

Therefore,

area of the triangle = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × 6 × 4

area of the triangle = 24 / 2

area of the triangle = 12 ft²

Therefore,

area of the rectangle = l × w

where

Hence,

area of the rectangle =  8 × 5 = 50 ft²

Surface area of the triangular prism = 12(2) + 3(50)

Surface area of the triangular prism = 24 + 150

Surface area of the triangular prism = 174 ft²

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Answer:

$7200

step by step Explanation:

Cameron borrowed $18,000 at an interest rate of 10% for a period of 4 years. To calculate the interest, we can use the simple interest formula: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.

Plugging in the values, we get I = 18,000 * 0.10 * 4 = $7,200. Therefore, Cameron paid a total of $7,200 in interest over the 4-year period.

The probability that between 124 and 125​, inclusive are on time is approximately 0.0655.

Given:

The probability of a flight arriving on time is 0.88

Number of flights selected randomly = 145

Let X be the number of flights arriving on time.

(a) P(exactly 128 flights are on time)

Using the normal approximation to the binomial distribution, we have:

Mean, µ = np = 145 × 0.88 = 127.6

Standard deviation, σ = sqrt(np(1-p)) = sqrt(145 × 0.88 × 0.12) = 3.238

P(X = 128) can be approximated using the standard normal distribution:

z = (128 - µ) / σ = (128 - 127.6) / 3.238 = 0.1234

P(X = 128) ≈ P(z = 0.1234) = 0.4511

Therefore, the probability that exactly 128 flights are on time is approximately 0.4511.

(b) P(at least 128 flights are on time)

P(X ≥ 128) can be approximated as:

z = (128 - µ) / σ = (128 - 127.6) / 3.238 = 0.1234

P(X ≥ 128) ≈ P(z ≥ 0.1234) = 0.4515

Therefore, the probability that at least 128 flights are on time is approximately 0.4515.

(c) P(fewer than 124 flights are on time)

P(X < 124) can be approximated as:

z = (124 - µ) / σ = (124 - 127.6) / 3.238 = -1.1154

P(X < 124) ≈ P(z < -1.1154) = 0.1326

Therefore, the probability that fewer than 124 flights are on time is approximately 0.1326.

(d) P(between 124 and 125​, inclusive are on time)

P(124 ≤ X ≤ 125) can be approximated as:

z1 = (124 - µ) / σ = (124 - 127.6) / 3.238 = -1.1154

z2 = (125 - µ) / σ = (125 - 127.6) / 3.238 = -0.7388

P(124 ≤ X ≤ 125) ≈ P(-1.1154 ≤ z ≤ -0.7388) = P(z ≤ -0.7388) - P(z < -1.1154)

P(124 ≤ X ≤ 125) ≈ 0.1981 - 0.1326 = 0.0655

Therefore, the probability that between 124 and 125​, inclusive are on time is approximately 0.0655.

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