An norca es 300 passengers and ha s doors with a height of 74 in Heights of men

Question

An norca es 300 passengers and ha s doors with a height of 74 in Heights of men a era naty dstributed with a mean of 69. inand a standard deiation of28i Complete pats a) through a. If a male passenger is randomly selected, find the probabiity that he can fit through the doorway without bending The probablity 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 74 in The probablity is (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers, which result is more reievant the probability from part (a) or the probability from part (bj? Why? OA. The probability from part (a) is more relevant because it shows the proportion of male passengers that wil not need to bad O B. The probability from part (b) OC. The probability from part (a)is more relevant because t shows the proportion of D. The probability from part (b) s more relevant because shows ne proporton of male passengrshat-not reed to d. When considering the comfort and safety of passengers, why are women ignored in this case? will be less than the door height mean height of the male passergers will be less than the door height. ) is more relevant because it shows the proportion of fights where the mean height of the male passengers i flights where the them to bend when entering the airoraft. Therefore, it is more important that men net have to bend than t is important that women not have to men are generalily taller than women, it is more difficult for O B. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodan O C. There is no adequate reason to ignore women. A separate statistical analysis should be carred out for the case of women. bend. p greater proportion of women

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 69
standard Deviation ( sd )= 2.8
a.
P(X < 74) = (74-69)/2.8
= 5/2.8= 1.7857
= P ( Z <1.7857) From Standard Normal Table
= 0.9629
b.
mean of the sampling distribution ( x ) = 69
standard Deviation ( sd )= 2.8/ Sqrt ( 150 ) =0.2286
sample size (n) = 150
P(X < 74) = (74-69)/2.8/ Sqrt ( 150 )
= 5/0.2286= 21.8704
= P ( Z <21.8704) From Standard NOrmal Table
= 1
c.
Option B is the answer

reason: since our criteria is to consider Male gender,since male height is more than female in reality, if we build a door height that acceses an average of male height without bend is suffice
d.
Option A is the answer

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