A random sample of 100,000 credit sales in a department store showed an average sale of $87.25. From past data, it is known that the standard deviation of the population is $20.00. What is the 95% confidence interval of the population mean?
A) $87.22 to $87.28
B) $87.13 to $87.37
C) $19.97 to $20.03
D) $19.88 to $20.12

Question

Quizplus · Accepted Answer

For a 95% confidence interval, we need to find the z-score for 97.5% (since we want to divide the 5% alpha level into two tails). This corresponds to a z-score of 1.96. 
Using the formula for a confidence interval: 
CI = X̄ ± (z*σ/√n) 
where X̄ is the sample mean, z is the z-score, σ is the population standard deviation, and n is the sample size. 
Plugging in the values: 
CI = 87.25 ± (1.96*20/√100,000) 
Simplifying: 
CI = 87.25 ± 0.12 
So the 95% confidence interval is from $87.13 to $87.37.

A Random Sample of 100,000 Credit Sales in a Department