Question

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

62.9 in

and standard deviation

3.2 in

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

68.5 in

and standard deviation

3.3 in

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

57 in

and a maximum of

62 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 ___%

(Round to two decimal places as needed.)

b. If the height requirements are charged 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.

(Round to one decimal place as needed.)

Answer 1

a)

for normal distribution z score =(X-μ)/σx
mean μ=	68.5
standard deviation σ=	3.3

percentage of men who meet the height requirement is :

probability =P(57<X<62)=P((57-68.5)/3.3)<Z<(62-68.5)/3.3)=P(-3.48<Z<-1.97)=0.0244-0.0003=0.0241~ 2.41 %

b)

for 5th percentile critical value of z=-1.645

therefore corresponding value=mean+z*std deviation=63.1

the new height requirements are a minimum of 63.1 in and a maximum of 68.5 in