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,the probability that the average weight of the boxes will exceed 94 lbs.is:
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 here, which states that for a sample size n>30, the sampling distribution of the sample mean will be approximately normal with a mean of the population mean and a standard deviation of the population standard deviation/sqrt(n).

So, in this case, the mean of the sampling distribution will be 90 lbs and the standard deviation will be 24/sqrt(36) = 4 lbs.

Now, we need to find the probability that the sample mean will be greater than 94 lbs:

z = (94 - 90) / 4 = 1

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score greater than 1 is 0.1587.

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

A Manufacturing Company Measures the Weight of Boxes Before Shipping