Question

In: Statistics and Probability

8)   An airliner carries 150 passengers and has doors with a height of 75 in. Heights...

8)   An airliner carries 150 passengers and has doors with a height of 75 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 150 passengers are​ men, find the probability that the mean height of the 75 men is less than 75 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? choose one

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​ (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. When considering the comfort and safety of​ passengers, why are women ignored in this​ case? choose one

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. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.

C. Since men are generally taller than​ women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Solutions

Expert Solution

a) P(X < 75)

= P((X - )/ < (75 - )/)

= P(Z < (75 - 69)/2.8)

= P(Z < 2.14)

= 0.9838

b) P( < 75)

= P(( - )/() < (75 - )/())

= P(Z < (75 - 69)/(2.8/))

= P(Z < 18.56)

= 1

c) Option -A) The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend.

d) Option - 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 woman not have to bend.


Related Solutions

An airliner carries 50 passengers and has doors with a height of 75 in. Heights of...
An airliner carries 50 passengers and has doors with a height of 75 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. B. I f half of the 50 passengers are​ men, find the probability that the mean height of the 25 men is less than 75 in. C....
An airliner carries 250 passengers and has doors with a height of 75 in. Heights of...
An airliner carries 250 passengers and has doors with a height of 75 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 0.9838 ​(Round to four decimal places as​ needed.) b. If half of the 250 passengers are​ men, find the...
An airliner carries 150 passengers and has doors with a height of 76 in. Heights of...
An airliner carries 150 passengers and has doors with a height of 76 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. (Round to four decimal places as​ needed.) b. If half of the 150 passengers are​ men, find the probability that the mean...
an airliner carries 50 passengers and has doors with a height of 74 in. Heights of...
an airliner carries 50 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8in what is the probability? if half of 50 passengers are, find the probability that the mean height of the 25 men is less than 74in
An airliner carries 350 passengers and has doors with a height of 72 in. Heights of...
An airliner carries 350 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69 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 nothing. ​(Round to four decimal places as​ needed.) b. If half of the 350 passengers are​ men, find the...
an airline carries 200 passengers and has doors with a height of 78in. heights of men...
an airline carries 200 passengers and has doors with a height of 78in. heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8. if a male passenger is randomly selected find the probability that he can fit through the doorway without bending if half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 78in
11. Disney Monorail The Mark VI monorail used at Disney World has doors with a height...
11. Disney Monorail The Mark VI monorail used at Disney World has doors with a height of 72 in. Heights of men are normally distributed with a mean of 68.6 in. and a standard deviation of 2.8 in. (Source: based on Data Set 1 “Body Data” in Appendix B) a. What percentage of adult men can fit through the doors without bending? Does the door design with a height of 72 in. appear to be adequate? Explain. b. What doorway...
10) The overbooking problem: A plane has a capacity of 150 passengers. The airline, which knows...
10) The overbooking problem: A plane has a capacity of 150 passengers. The airline, which knows that the industry standard is that one person out of 12 is a no-show at the airport, sells 160 tickets. a) What is the probability that all the passengers that show up at departure will be accommodated? b) What is the maximum number of tickets that the airline should sell so that they should be able to accommodate all the passengers with probability at...
An elevator has a placard stating that the maximum capacity is 1328 lb--8 passengers. So, 8...
An elevator has a placard stating that the maximum capacity is 1328 lb--8 passengers. So, 8 adult male passengers can have a mean weight of up to 1328/8=166 pounds. If the elevator is loaded with 8 male passengers, find the probability that it is overloaded because they have a mean weight greater than 166 lb. (Assume that weights of males are normally distributed with a mean of 173 lb and a standard deviation of 29 lb.) Does this elevator appear...
A bond with a face value of $1,000 has 8 years until maturity, carries a coupon...
A bond with a face value of $1,000 has 8 years until maturity, carries a coupon rate of 7.0%, and sells for $1,085. a. What is the current yield on the bond? (Enter your answer as a percent rounded to 2 decimal places.) b. What is the yield to maturity if interest is paid once a year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.) c. What is the yield to maturity...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT