Question

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?

Answer 1

Answer:

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;

$P(X=r)=\binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=01,2,3,......$

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) =  $n \times p$

                                          =  $600 \times 0.87$ = 522

Also, the standard deviation of X, S.D.(X)  =  $\sqrt{n \times p \times (1-p)}$

                                                                     =  $\sqrt{600 \times 0.87 \times (1-0.87)}$

                                                                     =  8.24