Chapter 12, Problem 25PT4

To determine

To identify: The correct statements among a, b, c, and d given below given that the weight distribution of a certain type of pigs is skewed to the right with a mean of 280 pounds and standard deviation of 80 pounds. A random sample of 100 pigs is taken.

1. It will be normally distributed with a mean of 280 pounds and standard deviation of 80 pounds.
2. It will be normally distributed with a mean of 280 pounds and standard deviation of 80 pounds.
3. It will be approximately normally distributed with a mean of 280 pounds and standard deviation of 80 pounds.
4. It will be approximately normally distributed with a mean of 280 pounds and standard deviation of 8 pounds.
5. There is no enough information to determine the mean and standard deviation of sampling distribution.

Answer to Problem 25PT4

(a) Correct option is (d) It will be approximately normally distributed with a mean of 280 pounds and standard deviation of 8 pounds.

Explanation of Solution

As per the central limit theorem, the distribution of any sample mean tends to normal distribution with a mean of µ and standard deviation when population has a mean of µ and standard deviation of σ as sample size tends to ∞.

1. The distribution of weight of pigs is right skewed and hence we can say that sample mean tends to normal distribution with a mean of 280 pounds and standard deviation =8 .Hence we can say that sample mean will be approximately normally distributed with a mean of 280 pounds and standard deviation of 8 pounds.