A group of students collected data at the Cedar Point amusem

A group of students collected data at the Cedar Point amusement park and reported that the “wait time” to ride the “Top Thrill Dragster” roller coaster ranged from 40 minutes to 90 minutes.

a. What is the probability that a person will wait between 50 and 60 minutes?

b. What is the probability a person will wait less than 60 minutes?

Solution

uniform distrubution X follows U(40,90)

the distrubution function is

F_X(x)= x-a/b-a

        =x-40/50-90

        =x-40/40

(a)

p[50<x<60]     = p[x<60]-p[x<50]

                         =F_x(60)-F_x(50)

                         =60-40/40-50-40/40

                         =20/40-10/40

                         =1/2-1/4

                         =0.5-0.25

                         =0.25

        p[50<x<60]=0.25

(b)

p[x<60]=F_x(60)

            =60-40/40

            =20/40

           =1/2

           =0.5

p[x<60]=0.5