Answer: Mean = 760
Standard deviation = 6.16
Step-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 .
