Question

a random sample of 200 farm-raised turkey       (N(30, 8)).

1. According 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

1:

Here we have

From above we have

According to empirical rule, 95% data values lie within 2 standard deviations of mean. That is 95% data values lies between 14 and 46.

2:

Sample size: n=200

The average of your sample is

$mu_{ar{x}}=mu=30$

3;

The standard deviation of your sample is

The standard deviation of sample is different from population standard deviation because samples have more variations in comparison to population.