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

Answer 1

Solution:

Given that :P=0.7

n=12

Let (X) be the number of cars that pass the inspection ,then the random variable x follows the binomial distribution with the parameters.

Let we have to find out the standard deviation=

=

=1.58

Within one standard deviation of the expected value means:

=(8.4-1.6,8.4+1.6)

=(6.8,10)

p(6.8<x<10)=p(x=7)+p(x=8)+p(x=9)+p(x=10)

=0.1585+0.2311+0.2397+0.1678

=0.7971

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)