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?

Mean = 760

Standard deviation = 6.16

Step-by-step explanation:

Given : The number of trials:

The probability that  a certain protection system will be recovered :

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

, 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 :-

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

5

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: