Question

according to insurance records a car with a certain protection system will be recovered 89 percent of the time. If 300 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen

Answer 1

The mean number of cars recovered after being stolen is 267 and the standard deviation is 5.42.

Explanation:

For each stolen car, there are only two possible outcomes. Either it is recovered, or it is not. The probability of a stolen car being recovered is independent of other stolen cars. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

`E(X) = np`

The standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p))`

In this problem, we have that:

`n = 300, p = 0.89`

So

`E(X) = np = 300*0.89 = 267`

`√(V(X)) = √(np(1-p)) = √(300*0.89*0.11) = 5.42`

The mean number of cars recovered after being stolen is 267 and the standard deviation is 5.42.