Question

Case 2:

Kellogg Corporation

Population mean weight is 360 grams with a standard deviation of 15 grams.

The quality analyst conducts a random sampling of 16 boxes found to have a sample mean weight of 370 grams.

By Sampling 16 boxes, the sample mean weight is 370 grams.

A. What is the Sampling error?

B. What is the sample standard error of the Sample mean?

Quality analyst would like to reduce the sampling error of the sample mean to One Gram? How many samples he need to study?

What is the Probability of weight of cereal is more than 370 grams with a sample size of 16 boxes?

Answer 1

a) sampling error = difference between population mean and sample mean
= 370-360 = 10

b)
standard error = sigma/sqrt(n) = 15/sqrt(16) = 15/4 = 3.75

c)
sampling error can be reduced by increasing sample size

15/sqrt(n) = 1
n = 225

d)
P(Xbar > 370)
= P(Z > (370 - 360)/3.75)
= P(Z > 2.6666)
= 0.0038

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