A small business ships specialty homemade candies to anywhere in the world. Past records indicate that orders weigh an average of 118 grams with a standard deviation of 14 grams. Suppose a random sample of 50 current orders is selected and each weighed.
a. Describe the sampling distribution of the sample mean by naming the model and telling its mean and standard deviation.
b. Suppose the resulting sample mean is 110 grams. Do you think that this sample result is unusually small? Explain.

Question

Quizplus · Accepted Answer

The Answer is a. We have a random sample of shipments drawn from a much larger population. With a sample of size 50 the CLT says that the approximate sampling model of the sample means will be N (118, 1.98).
b. A sample mean of only 110 grams is about 4 standard deviations below what we expect, a very unusual result.

A Small Business Ships Specialty Homemade Candies to Anywhere in the World