The weights for a population of North American raccoons have a bell-shaped frequency curve with a mean of about 12 pounds and a standard deviation of about 2.5 pounds.
About 95% of the mean weights from samples of size 100 raccoons from this population fall between what two values?
A) 11.75 and 12.25
B) 11.5 and 12.5
C) 2.5 and 12
D) 7 and 17
E) 9.5 and 14.5

Question

Quizplus · Accepted Answer

We know that the mean is 12 pounds and the standard deviation is 2.5 pounds.

For a sample of size n, the standard error (SE) is given by:

SE = standard deviation / sqrt(n)

SE = 2.5 / sqrt(100) = 0.25

We are asked to find the range that contains 95% of the mean weights from samples of size 100 raccoons.

We can use the fact that for a normal distribution, 95% of the values fall within 1.96 standard errors of the mean.

So the range would be:

12 - 1.96(0.25) to 12 + 1.96(0.25)

11.5 to 12.5

Thus, the best choice is B.

The Weights for a Population of North American Raccoons Have