A company wants determine the sales of single house models, called Cottage. Sale

Question

A company wants determine the sales of single house models, called Cottage. Sales estimate is based on demand for various types of single home models. Overall demand is normally distributed with a mean of 3 million units, standard deviation or 500,000 units. The share of the "cottage"house is assumed to be 4%. After running 1,000 simulated scenarios, a 95% confidence interval was conducted for sales for "Cottage" sold with limits of 93,048 and 146, 964.

a. If the mean was increased to 6 million, how would the confidence interval change?

b. If the Standard deviation was changed to 250,000, what would happen to the confidence interval?

Explanation / Answer

Lower limit of confidence interval: 93048

Upper limit of confidence interval: 146964

a)

The margin of error is

ME = (146964 - 93048) /2 = 26958

The new confidence interval is

6000000 +/- 26958 =(5973042, 6026958)

The width of confidence interval remain same but it is shifted to upward.

b)

In margin of error of standard deviation come into numerator so as the standard deviation decreases margin of error also decreases.

That is confidence interval becomes narrower.

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