Question

According to police​ sources, a car with a certain protection system will be recovered 92 % 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? Round the answers to the nearest hundredth.

Answer 1

Answer:

552; 6.6452 (approx)

Explanation:

Given that,

Car recovered, p = 92% of the time

Number of cars stolen, n = 600 (randomly selected)

Probability of not recovering: (1 - p) = 1 - 0.92

                                                          = 0.08

Mean = Number of observations × Probability of recovering

         = 600 × 0.92

         = 552

Standard deviation:

$= \sqrt{n\times p\times (1-p)}$

$= \sqrt{600\times 0.92\times 0.08}$

$=\sqrt{44.16}$

= 6.64529909

Therefore, the mean and standard deviation of the number of cars recovered after being​ stolen is 552 and 6.6452(approx), respectively.