Q:

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?

Accepted Solution

A:
Answer: Mean = 760 Standard deviation = 6.16Step-by-step explanation:Given : The number of trials: [tex]n=800[/tex]The probability that  a certain protection system will be recovered :[tex]p=0.95[/tex]We know that the mean and standard deviation of binomial distribution is given by :_[tex]\text{Mean}=np[/tex][tex]\text{Standard deviation}=\sqrt{np(1-p)}[/tex], 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 :-[tex]\text{Mean}=800\times0.95=760[/tex][tex]\text{Standard deviation}=\sqrt{800\times0.95(1-0.95)}\\\\=6.164414002\approx6.16[/tex]Hence, the mean is 760 and standard deviation is 6.16 .