Of all cars on the interstate 80 exceed the speed limit What

Of all cars on the interstate, 80% exceed the speed limit. What proportion of speeders might we see among the next 50 cars? Check the necessary conditions and describe the sample distribution.

Solution

The distribution here is binomial with p=0.8,n=50. Since n is large, we can approxmate this to the normal distribution.

np=40

sd(p)=sqrt(pq/n)=0.057

we use the probability law of normal distribution and find that 68% of the samples have proportion of speeders between 0.743 and 0.857, 95% of them have speeders between 0.686 and 0.914 and 99.9% of them have speeder between 0.629 and 0.971.