A major shipping company has stated that 96 percent of all parcels are delivered on time. To check this, a random sample of n = 200 parcels were sampled. Of these, 184 arrived on time. If the company's claim is correct, what is the probability of 184 or fewer parcels arriving on time?
A) About 0.0019
B) Nearly 0.24
C) Just over 0.98
D) About 0.4981

Question

Quizplus · Accepted Answer

The probability can be calculated using a normal approximation to the binomial distribution. With p = 0.96, n = 200, the mean is np = 192, and the standard deviation is sqrt(np(1-p)) = sqrt(7.68). The z-score for 184 is (184-192)/sqrt(7.68) ≈ -2.89. Using standard normal distribution tables, the probability of a z-score of -2.89 or less is approximately 0.0019.

A Major Shipping Company Has Stated That 96 Percent of All