A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for $\mu$ is
A)105.0 to 225.0
B)175.0 to 185.0
C)100.0 to 200.0
D)170.2 to 189.8

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for the population mean:

CI = X̄ ± Z * (σ/√n)

Where:
X̄ = sample mean = 180
σ = population standard deviation = 75
n = sample size = 225
Z = z-score for the desired confidence level = 1.96 (for 95% confidence level)

Plugging in the values, we get:

CI = 180 ± 1.96 * (75/√225) 
CI = 180 ± 1.96 * 5 
CI = 180 ± 9.8

So the 95% confidence interval for the population mean is:

CI = (180 - 9.8, 180 + 9.8)
CI = (170.2, 189.8)

Therefore, the best choice is D, with the above explanation.

A Sample of 225 Elements from a Population with a Standard