The average age of vehicles registered in the United States

The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

Select one:

a. 5.2%

b. 28.8%

c. 15.7%

d. 6.4%

e. Cannot be determined

Solution

mu = average age = 96 months

sigma = 15

n = sample size = 36

Std error of sample = 15/rt 36 = 15/6 = 2.5

As x is normal

P(98<x<100) = P(2/2.5 <z<4/2.5)

=P(0.8<z<1.6) =0.4452-0.2881

= 0.1571

Hence in percent it is 15.7%

c is right answer