Question

According to insurance records, a car with a certain protection system will be recovered 95% of the time. If 800 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen?

Answer 1

Answer: Mean = 760

Standard deviation = 6.16

Step-by-step explanation:

Given : The number of trials: $n=800$

The probability that  a certain protection system will be recovered :$p=0.95$

We know that the mean and standard deviation of binomial distribution is given by :_

$\text{Mean}=np$

$\text{Standard deviation}=\sqrt{np(1-p)}$, where n is the number of trials and p is the probability of success.

Now, the mean and standard deviation of the number of cars recovered after being stolen is given by :-

$\text{Mean}=800\times0.95=760$

$\text{Standard deviation}=\sqrt{800\times0.95(1-0.95)}\\\\=6.164414002\approx6.16$

Hence, the mean is 760 and standard deviation is 6.16 .