Question

An airliner carries 50 passengers and has doors with a height of 70 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in.

a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.

Answer 1

The probability that a male passenger can fit through the doorway without bending is approximately 64.54%.

Step-by-step explanation:

To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the z-score of the height of the doorway. The z-score is calculated as (doorway height - mean height) / standard deviation. In this case, the mean height is 69.0 in and the standard deviation is 2.8 in.

Let's calculate the z-score for the doorway height of 70 in:

z = (70 - 69.0) / 2.8 = 0.3571

Next, we need to find the area under the normal distribution curve to the left of this z-score. Using a standard normal distribution table or a calculator, we can find that the area to the left of 0.3571 is approximately 0.6454.

Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.6454 or 64.54%.