Question

Weights of farm-raised turkeys are distributed N(30, 8) (in lbs.).

1. to the empirical rule, how many of the values do you expect to be less than 14 or greater than 46? Briefly explain your answer.

2. Since the weights are distributed N(30, 8), we say that we expect the average weight of a sample of farm-raised turkey to be 30 lbs.; that is, 30 is the expected value (also, the mean) of the distribution. What is the average of your sample? Briefly explain (in one word) why it is not exactly equal to 30.

3. What is the standard deviation of your sample? What did you expect the standard deviation of your sample to be? Briefly explain (in one word) why the standard deviation of your sample is not exactly equal to what you expected.

Answer 1

3) The standard deviation of the sample is

$s=\sqrt{\frac{1}{n-1}\sum (x_{i}-\bar{x})^{2}}$

The expected standard deviation of the sample to be

$E(s)=\sigma/\sqrt{n}=\sqrt{8}/\sqrt{n}$

The sample standard deviation uses only a subset of the population mean. Hence, the standard deviation of the sample is not exactly equal to what you expected.