Question

#6 a survey found that women’s heights are normally distributed with mean 62.2 in. and standard deviation 2.7 in, the survey also found that men’s heights are normally distributed with a mean 68.7in. and standard deviation 2.8. a. most of the live characters at an amusement park have height requirements with a minimum of 4ft. 8in. and a maximum of 6ft. 3in. find the percentage of women meeting the height requirement, b finds the percentage of men meeting the height requirement, c if the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women, what are the new height requirements? The new height requirements are at least---in. and at most----in.

Answer 1

4ft 8 in = 56 inch

6 ft 3 in = 75 inch

a)The percentage of woment who meet the height requirement is given by area under the Z curve between points Xbar = 56 and 75

Z = (x-µ)/σ

b)

The percentage of men who meet the height requirement is given by area under the Z curve between points Xbar = 56 and 75

c)

Tallest 5% men

p = 0.95

Z = 1.645

1.645 = (Xbar - 68.7)/2.8

X bar = 73.306 inches

Shortest 5% women

p = 0.05

Z = -1.645

-1.645 = (Xbar - 62.2)/2.7

X bar = 57.76 inches

The new height requirements are at least 57.76 in and at most 73.31 inch