Question

A survey found that​ women's heights are normally distributed with mean 62.6 in. and standard deviation 2.7 in. The survey also found that​ men's heights are normally distributed with mean 68.5 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 64 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 nothing​%. ​(Round to two decimal places as​ needed.) Since most men ▼ do not meet meet the height​ requirement, it likely that most of the characters are ▼ men. 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 nothing in. and a maximum of nothing in. ​(Round to one decimal place as​ needed.)

Answer 1

a)

percentage of men meeting the height requirement =P(57 <X<64)=P(-3.19 <Z<-1.25)=0.1056-0.0007 =0.1049~ 10.49%

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

b)

new height​ requirements are a minimum of 62.6 and 68.5 inch