Chapter 7 The Sampling Distribution of the Mean and EXCEL Probability Calculations

From William E. Becker, Statistics for Business and Economics Using Microsoft Excel 97, S.R.B. Publishing, 1997, p. 263. Reproduced with permission of S.R.B. Publishing.

QUERY 7.16 (p. 263.): A bakery sells an average of 24 loaves of bread per day. Sales (x) are normally distributed with a standard deviation of four.

a. If a random sample of size n = 1 (day) is selected, what is the probability this x value will exceed 28?

b. If a random sample of size n = 4 (days) is selected, what is the probability that will exceed 28?

c. Why does the answer in part a differ from that in part b?

ANSWER: a. The sampling distribution of the sample mean (

) is normal with a mean of 24 and a standard error of the mean of 4

Thus,

Or using EXCEL, 0.15866 =1-NORMDIST(28,24,4,1)

b. The sampling distribution of the sample mean () is normal with a mean of 24 and a standard error of the mean of 2Thus,

Or using EXCEL, 0.02275 =1-NORMDIST(28,24,2,1)

c. The sample size is 1 in a and 4 in b. If n=1, the sampling distribution of the sample mean is just the population distribution itself. With a larger size sample, sampling distribution of the sample mean has smaller standard deviation than that in the population.

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