If the mean of a random sample of size 400 is used to estimate the mean of an infinite population with a standard deviation of 60 , the probability is 0.95 that the error is less than
A) 1.96 .
B) 117.6 .
C) 3.92 .
D) 5.88 .

Question

Quizplus · Accepted Answer

The margin of error in estimating the population mean with a 95% confidence level is given by $Z \times \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the confidence level (1.96 for 95%), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the values: $1.96 \times \frac{60}{\sqrt{400}} = 1.96 \times 3 = 5.88$.

If the Mean of a Random Sample of Size 400