Question

a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is (Round to four decimal places as needed.) b. If half of the 150 passengers are men, find the probability that the mean height of the 75 men is less than 78 in. The probability is (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? A. The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend. B. The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height. C. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend. D. The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height. d. When considering the comfort and safety of passengers, why are women ignored in this case? A. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women. B. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Answer 1

To find the probability that a male passenger can fit through the doorway without bending, we need to calculate the z-score and look it up in the standard normal distribution table. To find the probability that the mean height of 75 men is less than 78 inches, we need to calculate the standard error of the mean and use the t-distribution. Comparing the probabilities will determine which result is more relevant.

Step-by-step explanation:

To find the probability that a male passenger can fit through the doorway without bending (part a), we need to determine the proportion of men who are shorter than the doorway height. We are given that the mean height of the male population is 69 inches with a standard deviation of 2.8 inches. We can use the standard normal distribution to calculate the probability.

1. Calculate the z-score using the formula: z = (x - mean) / standard deviation, where x is the doorway height.
2. Look up the z-score in the standard normal distribution table to find the corresponding probability.
3. Round the probability to four decimal places.

To find the probability that the mean height of the 75 men is less than 78 inches (part b), we need to calculate the standard error of the mean and use the t-distribution. Then, we can look up the probability in the t-distribution table. We can also compare the probabilities from parts (a) and (b) to determine which is more relevant for considering comfort and safety of passengers.