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# Statistics: Probability Calculations

1. An airliner carries 50 passengers and has door with a height of 70in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8in.
a. If an male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
The probability is _______
b. if half of the 50 passengers are men, find the probability that the mean height of the 25 men is less than 70 in.
The probability is _____
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 (b) is more relevant because it show 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 show the proportion of male passengers that will not need to bend
d) 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.
d. When considering the comfort and safety of passengers, why are women ignored in this case?
a) Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.
b) There is no adequate reason to ignore a women. A separate statistical analysis should be carried out for the case of women.
c) 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.

2. a) With n=11 and p=0.7, find the binomial probability P(5) by using a binomial probability table. (b) if np ? and nq ? 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial; if <5 or nq <5, then state that the normal approximation cannot be used.
a. find the probability by using a binomial probability table.
P(5)=___________ (round to three decimal places as needed)
b. Select the correct choice below and, if necessary, fill in the anser line to complete your choice
a) P(5) = _______ (round to four decimal places as needed)
b) The normal distribution cannot be used

#### Solution Summary

The solution answers the various probability calculations in the attachments provided.

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