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 lbs.and 24 lbs. ,respectively,then based on a sample size of 36 boxes,what is the probability that the average weight of the boxes will exceed 94 lbs.?
A)34.13%
B)84.13%
C)15.87%
D)56.36%
E)16.87%

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the sampling distribution of the sample mean.

The mean of the sampling distribution of the sample mean is equal to the population mean, which is 90 lbs.

The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size:

σ/√n = 24/√36 = 4

So the z-score for a sample mean of 94 lbs is:

z = (94 - 90) / 4 = 1

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than 1:

P(Z > 1) = 0.1587

Therefore, the probability that the average weight of the boxes will exceed 94 lbs is 15.87%.

The closest answer choice is C.

A Manufacturing Company Measures the Weight of Boxes Before Shipping