The probability that a rental car will be stolen is 0.001.If 25,000 cars are rented from Hertz,what is the normal approximation to the probability that fewer than 20 will be stolen?
A)0.2577
B)0.1335
C)0.1128
D)0.8335

Question

Quizplus · Accepted Answer

Let X be the number of stolen rental cars out of 25,000. Since np = 25,000*0.001 = 25 > 10 and n(1-p) = 25,000*0.999 = 24,975 > 10, we can use the normal approximation to the binomial distribution. 
The mean and standard deviation of X are:
μ = np = 25
σ = sqrt(np(1-p)) = 4.987.
To find the probability that fewer than 20 cars are stolen, we standardize the random variable:
z = (19.5 - 25) / 4.987 ≈ -1.106,
where we use the continuity correction. 
Using a standard normal table, we find the probability to be approximately 0.1335. Therefore, choice B is the best answer.

The Probability That a Rental Car Will Be Stolen Is