A pharmaceutical company wanted to estimate the population mean of monthly sales for their 250 sales people. Forty sales people were randomly selected. Their mean monthly sales were $10,000 with a standard deviation of $1,000. Construct a 95% confidence interval for the population mean.

Question

Quizplus · Accepted Answer

Since the sample size (n=40) is greater than 30 and we have the population standard deviation, we can use the z-distribution to construct the confidence interval. 
The critical value for a 95% confidence level with 39 degrees of freedom (n-1) is 1.96. 
The margin of error is 1.96 * (1000/sqrt(40)) = 306. 
The confidence interval is therefore (10000-306, 10000+306), which simplifies to (9706, 10294). Therefore, the best choice is B.

A Pharmaceutical Company Wanted to Estimate the Population Mean of Monthly