Question

To work as a flight attendant, you must be between 5ft 3 in and 6ft tall. The height of 18-24 year-old females is normally distributed with a mean of about 67.3 inches and a standard deviation of 2.1 inches.
[Hint:Convert feet into inches (1ft = 12 in)]


a) What is the percent of women ages 18-24 who are between 5ft 3 in and 6ft? %


b)What height represents 87 th percentile?


c)What is the probability that a female who is 18-24 years old is taller than 5ft 6 in?Round this to 4 decimal places

Answer 1

Given that, mean = 67.3 inches

standard deviation = 2.1 inches

a) 5ft 3 in = (12 * 5) + 3 = 60 + 3 = 63 in

6 ft = (12 * 6) = 72 in

Therefore, 96.73% of women ages 18-24 who are between 5ft 3 in and 6ft.

b) We want to find, the value of x such that, P(X < x) = 0.87

Therefore, 87th percentile is 69.67 in.

c) 5ft 6 in = (12 * 5) + 6 = 60 + 6 = 66 in

Therefore, the probability that a female who is 18-24 years old is taller than 5ft 6 in is 0.7324