Question

An airliner carries 400 passengers and has doors with a high of 72 inches. Heights of men are normally distributed with a mean of 69 and a standard deviation of 2.8 inches. Complete parts a through d.

(A) the probability is

(B) if half of the 400 passengers are men find the probability that the mate mean height of the 200 man is less than 72 inches

(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

(D) when considering the comfort and safety of passengers why are women ignored in this case

Answer 1

a)

here question is not given ; I think it is probabiliy of a person to have height less than 72 ' please revert:

for normal distribution z score =(X-μ)/σ
here mean=       μ=	69
std deviation   =σ=	2.800

hence P( having height less than 72):

probability =

P(X<72)

=

P(Z<1.07)=

0.8577

b)

sample size       =n=	200
std error=σx̅=σ/√n=	0.1980

probability =

P(X<72)

=

P(Z<15.15)=

1.0000

c)

here part a is more important as we need to check for an individual person comfort ; not the average of these people,

d)

as it is assumed that mean height of women might be less than men; therefore if it is  comfortable and safe for male ; it should be comfortable and safe for female.