Concept explainers
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
- It will be
normally distributed with a mean of 280 pounds and standard deviation of 80 pounds. - It will be normally distributed with a mean of 280 pounds and standard deviation of 80 pounds.
- It will be approximately normally distributed with a mean of 280 pounds and standard deviation of 80 pounds.
- It will be approximately normally distributed with a mean of 280 pounds and standard deviation of 8 pounds.
- 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
- 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.
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