Question

The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 inches. Heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 72 inches.

a)0.0001

b)0.8577

c)0.9999

d)0.1432

Answer 1

To find the probability that the mean height of the 100 men is less than 72 inches, we need to calculate the z-score for the mean height of 72 inches using the population mean and standard deviation of the heights of men. Then, we can find the probability using the standard normal distribution table. The probability is approximately 0.8577.

Step-by-step explanation:

To find the probability that the mean height of the 100 men is less than 72 inches, we need to calculate the z-score for the mean height of 72 inches using the population mean and standard deviation of the heights of men. Then, we can find the probability using the standard normal distribution table.

First, we find the z-score:

z = (x - μ) / σ

where:

x = mean height of 72 inches

μ = population mean of 69 inches

σ = population standard deviation of 2.8 inches

Substituting the values, we get:

z = (72 - 69) / 2.8 ≈ 1.071

Next, we use the standard normal distribution table to find the probability associated with a z-score of 1.071, which is approximately 0.8577.

Therefore, the probability that the mean height of the 100 men is less than 72 inches is approximately 0.8577.

Answer 2

C.) 0.9999

Step-by-step explanation:

"It just works."