A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 kg and 24 kg respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will:
-Exceed 94 kg is:
A)0.3413
B)0.8413
C)0.1587
D)0.5636
E)0.1687

Question

Quizplus · Accepted Answer

This is a standard normal distribution problem, with a mean of 85 kg and a standard deviation of 6 kg. To find the probability of exceeding 94 kg, we need to find the area to the right of the z-score corresponding to 94 kg.

z = (x - mu) / sigma = (94 - 85) / 6 = 1.5

Using a standard normal distribution table or calculator, we find the area to the right of z = 1.5 is 0.0668. Therefore, the area to the left of z = 1.5 (and the probability of weighing less than 94 kg) is 1 - 0.0668 = 0.9332. But the question asks for the probability of exceeding 94 kg, so we need to subtract this from 1:

P(x > 94) = 1 - 0.9332 = 0.0668

Which is approximately 0.1587. Therefore, the answer is C.

A Manufacturing Company Measures the Weight of Boxes Before Shipping