The sample size needed to estimate a population mean within 1.5 units with a 95% confidence when the population standard deviation equals 10 is:
A) 121
B) 13
C) 171
D) 54
E) 88

Question

Quizplus · Accepted Answer

The formula to calculate the sample size when estimating the population mean with a known standard deviation and confidence interval is:

n = [(Z-value)^2 * (Population standard deviation)^2] / (margin of error)^2

Using a confidence level of 95%, the Z-value is 1.96 (found using a Z-table or calculator). 
Plugging in the given values, we get:

n = [(1.96)^2 * (10)^2] / (1.5)^2 = 170.67

Rounding up to the nearest whole number gives us a sample size of 171. Therefore, the answer is C.

The Sample Size Needed to Estimate a Population Mean Within