SOLUTION: The weights of people in a certain population are normally distributed with a mean of 154 lb and a standard deviation of 23 lb. (a)Determine the distribution of the sample mean

Question 1108910: The weights of people in a certain population are normally distributed with a mean of 154 lb and a standard deviation of 23 lb.
(a)Determine the distribution of the sample mean and standard deviation for samples of size 4.
(b)Commenton whether the distribution of the mean is normal or approximately normal. Justify your answer.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The sample mean for samples of size 4 (or any other size) is 154, same as the population.
The standard error is sigma/sqrt(n)=23/sqrt(4) or 11.5
The mean is normally distributed (of the sample) because the original population is normally distributed, not approximately normally distributed.
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