The average amount of students who ride the bus each year in

The average amount of students who ride the bus each year in Wilton Iowa is 60 students. The standard deviation for this is 5 students. Find the probability that next year Wilton will have the following amounts of students riding the bus. Assume this is a normally distributed problem.

a. Less than 58 students

b. More than 62 students

c. Between 50 and 60 students

Solution

a)

z = (58 -60)/5 = -0.4

P(X<58) = 0.3446 Answer

b)

z = (62 -60)/5 = 0.4

P(X>62) = 1 - 0.6554 = 0.3446 Answer

c)

z1 = (50 -60)/5 = -2.0

P(X<50) = 0.0228

z2 = (60 -60)/5 = 0

P(X<60) = 0.5

Therefore,

P(50<x<60) = 0.5 - 0.0228 = 0.4772 Answer