According to insurance records, a car with a certain protection system will be recovered 87% of the time. If 600 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen?

The mean and standard deviation of the number of cars recovered after being stolen is 522 and 8.24 respectively.

Step-by-step explanation:

We are given that according to insurance records, a car with a certain protection system will be recovered 87% of the time.

Also, 600 stolen cars are randomly selected.

Let X = Number of cars recovered after being stolen

The above situation can be represented through binomial distribution;

where, n = number of trials = 600 cars

            r = number of success

            p = probability of success which in our question is the probability

                    that car with a certain protection system will be recovered,

                     i.e. p = 87%.

So, X ~ Binom(n = 600, p = 0.87)

Now, the mean of X, E(X) =  

                                          =   = 522

Also, the standard deviation of X, S.D.(X)  =  

                                                                     =  

                                                                     =  8.24