Question

A survey found that​ women's heights are normally distributed with mean

62.5

in. and standard deviation

3.4

in. The survey also found that​ men's heights are normally distributed with mean

67.9

in. and standard deviation

3.3

in. Most of the live characters employed at an amusement park have height requirements of a minimum of

56

in. and a maximum of

63

in. Complete parts​ (a) and​ (b) below.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​ park?

The percentage of men who meet the height requirement is 6.94%.

​(Round to two decimal places as​ needed.)

Since most men

do not meet the height​ requirement, it is likely that most of the characters are women.

b. If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements?

The new height requirements are a minimum of ____in. and a maximum of ____in.

Answer 1

a)

probability =P(56<X<63)=P((56-67.9)/3.3)<Z<(63-67.9)/3.3)=P(-3.61<Z<-1.48)=0.0694-0.0002=0.0692~ 6.92%

b)

for 5th percentile critical value of z=		-1.645
therefore corresponding value=mean+z*std deviation=			62.47~62.5 inch

for 50th percentile critical value of z=		0.000
therefore corresponding value=mean+z*std deviation=			67.9 inch

The new height requirements are a minimum of 62.5 inch and a maximum of 67.9 inch

(please try 62.47 if required till 2 decimals instead of 62.5)