Data Set 8-7: A population with a mean (µ) of 10 and a standard deviation ($\sigma$) of 1. (Carry 3 or 4 decimals in your calculations.)
-See Data Set 8-7. If N = 3, what proportion of the means of a sampling distribution would be larger than 12?
A) .4772
B) .0228
C) .4997
D) .0003
E) .4986
F) .0014
G) .4927
H) .0073

Question

Quizplus · Accepted Answer

To find the proportion of the means of a sampling distribution that would be larger than 12, we use the formula for the standard error of the mean, which is the standard deviation divided by the square root of the sample size (N). Here, the standard deviation (σ) is 1, and N = 3. The standard error (SE) = σ / sqrt(N) = 1 / sqrt(3) ≈ 0.5774. We then calculate the z-score for a mean of 12 using the formula z = (X - µ) / SE, where X is the mean we're comparing to the population mean (µ), which is 10. So, z = (12 - 10) / 0.5774 ≈ 3.464. Looking up this z-score in a standard normal distribution table or using a calculator, we find that the proportion of the area under the curve to the right of this z-score (which represents the proportion of means larger than 12) is approximately 0.0003.

Data Set 8-7: a Population with a Mean (µ) of 10