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

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

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}* p^(r) * (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 * p`

=
`600 * 0.87` = 522

Also, the standard deviation of X, S.D.(X) =
`√(n * p * (1-p))`

=
`√(600 * 0.87 * (1-0.87))`

= 8.24