An airliner caries 300 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. Complete parts (a) through (d). 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 300 passengers are men, find the probability that the mean height of the 150 men is less than 70 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. O C. 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. O D. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend. d. When considering the comfort and safety of passengers, why are women ignored in this case? O A Since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. Therefore, it is more important that men not have to bend than it is important that women not have to bend. O 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. O C. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.
An airliner caries 300 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. Complete parts (a) through (d). 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 300 passengers are men, find the probability that the mean height of the 150 men is less than 70 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. O C. 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. O D. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend. d. When considering the comfort and safety of passengers, why are women ignored in this case? O A Since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. Therefore, it is more important that men not have to bend than it is important that women not have to bend. O 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. O C. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**Airliner Passenger Heights and Doorway Comfort**
An airliner carries 300 passengers and has doors with a height of 70 inches. Heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.
**Tasks:**
a. **Probability for Individual Male Passenger:**
1. Calculate the probability that a randomly selected male passenger can fit through the doorway without bending.
- The probability is ____.
- (Round to four decimal places as needed.)
b. **Probability for Mean Height of Male Passengers:**
1. Calculate the probability that the mean height of 150 male passengers is less than 70 inches.
- The probability is ____.
- (Round to four decimal places as needed.)
c. **Relevance to Comfort and Safety:**
1. Determine which probability is more relevant for passenger comfort and safety: part (a) or part (b)?
2. Provide reasoning for your answer.
- Options:
- A. 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.
- B. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
- C. 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. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
d. **Consideration of Women in Analysis:**
1. Explain why women are ignored in this case when considering the comfort and safety of passengers.
- Options:
- A. Since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. Therefore, it is more important that men not have to bend than it is important that women not have to bend.
- 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.
- C. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.
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