Please show work and formula used. An airliner carries 300 passengers and has do
ID: 3181346 • Letter: P
Question
Please show work and formula used.An airliner carries 300 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.85 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 0.8580 b. If half of the 300 passengers are man, find the probability that the mean height of the 150 men is less than 75 in. The probability is 1.0000. c. When considering the comfort and safety of passengers, which results 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 (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.
Explanation / Answer
a)z=(72-69)/2.8=1.0714.
we want P(Z<1.0714) from normal distribution table we have 85.8%.
b) Standard error of the mean is sigma/sqrt(n)
= 2.8 inches/sqrt(150) = 0.2286 inches
In this case, z = 3.0/0.2286 = about 13.1
we want P(z<13.1) so essientially it is 100%.
c) Obviously A as in question(b) half are mean(given) so no need to bend