An airliner carries 300 passengers and Heights of men are normally distrbuted wi

Question

An airliner carries 300 passengers and Heights of men are normally distrbuted with a mean of 690inand a standrd deation of 2an0 ws ta) (as a. if a male passenger is randomly selected, find the probability that he can it through the doonway without bending The probability 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 probability is Round to four decimal places as needed.) G. When considering the comfort and safety of passengers, which result is more relevant: the probablity from part (a) or the probability from part (b)? Why? A. The probability from part (a) is more relevant because " shows the proportion of male sengers Pat wil not need b bend O B. The probability from part(tb) is more relevant because it shows the proportion of fights wthere the meaun hneight of the male passengens all bo los han the door heign from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers wil be less than the door height O D· The probability from part 0b) is more relevant because it shows the proponon of male passengers that wa na need to bend d. When considering the comfort and safety of passengers, why are women ignored in this case? Since men are generally tallier than women, it is more difficult for them to bend when entering the aircrat. Therefore, t i bend more important hat men not have to bend ain t is important the O A. S O B. Since men are generally tler than women, a design that accommodates a sutable proportion of men wil necessanly accommodate a O C. There is no adequate reason to ignore women. A separate statistical analysis should be carmied out for the case 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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