Question

The average age of all vehicles registered in the united states is 96 months with the population standard deviation of 16 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 90 an 100 months. Group of answer choices 92.1% 93.3% 62.4% 12.2%

Answer 1

Solution :

Given that ,

mean =   = 96

standard deviation = = 16

n = 36

= 96

=  / n= 16/ 36=2.6667

P(90<     <100 ) = P[(90-96) / 2.6667 < ( - ) /   < (100-96) / 2.6667 )]

= P( -2.25< Z < 1.50)

= P(Z < 1.50) - P(Z <-2.25 )

Using z table

=0.9332-0.0122

=0.9210

answer=92.1%-