The probability that an appliance is in repair is .5.If an apartment complex has 100 such appliances,what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial.
A).5000
B).0287
C).6000
D).9713

Question

Quizplus · Accepted Answer

Using the normal approximation to the binomial, we can calculate the mean and standard deviation of the distribution as follows:
Mean = np = 100 x 0.5 = 50
Standard deviation = sqrt(np(1-p)) = sqrt(100 x 0.5 x 0.5) = 5
We want to find the probability that at least 60 appliances will be in repair. This is equivalent to finding the probability that the number of appliances in repair is greater than or equal to 60, which can be written as:
P(X >= 60) = P(Z >= (60 - 50) / 5)    [where Z is a standard normal variable]
P(Z >= 2) = 0.0228 (from standard normal table)
Therefore, the probability that at least 60 appliances will be in repair is approximately 0.0287 or choice B.

The Probability That an Appliance Is in Repair Is