Question

A new roller coaster at an amusement park requires individuals to be at least​ 4' 8"

​(56 inches) tall to ride. It is estimated that the heights of​ 10-year-old boys are normally distributed with

mu equals μ=55.0 inches and sigma equals σ=4 inches.

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

b. A smaller coaster has a height requirement of

50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?

Answer 1

µ = 55

sd = 4

a)

                             

                              = P(Z > 0.25)

                              = 1 - P(Z < 0.25)

                              = 1 - 0.5987

                              = 0.4013

b)

                             

                              = P(Z > -1.25)

                              = 1 - P(Z < -1.25)

                              = 1 - 0.1056

                              = 0.8944

c)

                                        

                                         = P(-1.25 < Z < 0.25)

                                         = P(Z < 0.25) - P(Z < -1.25)

                                         = 0.5987 - 0.1056

                                         = 0.4931