Question

Seventy percent of all vehicles examined at a certain emissions inspection station pass the
inspection. Suppose a random sample of 12 cars is selected. Assuming that successive vehicles
pass or fail independently of one another calculate each of the following.

a.)What is the expected number of vehicles to pass?

b.)What is the probability that the number of the 12 cars selected that pass is within one standard deviation of the expected value?

Answer 1

Solution:

We are given:

Let x be the number of cars that pass the inspection, then the random variable x follows the binomial distribution with parameters:

a.)What is the expected number of vehicles to pass?

Answer: The expected number of vehicles to pass is:

b.)What is the probability that the number of the 12 cars selected that pass is within one standard deviation of the expected value?

Answer: We have to first find the standard deviation as:

Within one standard deviation of the expected value means:

The excel function to find the P(x=7) is =BINOMDIST(7,12,0.7,FALSE)

The excel function to find the P(x=8) is =BINOMDIST(8,12,0.7,FALSE)

The excel function to find the P(x=9) is =BINOMDIST(9,12,0.7,FALSE)

The excel function to find the P(x=10) is =BINOMDIST(10,12,0.7,FALSE)