A continuous random variable x has a left-skewed distribution with a mean of 155 and a standard deviation of 28.The sampling distribution of the sample mean for a sample of 75 elements taken from this population is:
A)approximately normal
B)not normal
C)skewed to the right
D)skewed to the left

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (usually n > 30), regardless of the shape of the population distribution. Since the sample size is 75, the sampling distribution is approximately normal.

A Continuous Random Variable X Has a Left-Skewed Distribution with a Mean