# Distribution of sample means

Suppose the mean GPA of BYU-Idaho students is 3.5 and the standard deviation is 0.7. It is well known that this distribution is left- skewed. A random sample of n=81 students will be drawn. 1. What is the mean of the distribution of the sample means (sampling distribution)  for all possible samples of size 81 that could be drawn from the parent population?2. What is the standard deviation of the distribution of the sample means for all possible samples of size 81 that could be drawn from the parent population? 3.  What is the probability that the mean GPA for 81 randomly selected BYU-Idaho students will be less than 3.3?4. What is the probability that the mean GPA for 81 randomly selected BYU-Idaho student will be greater than 3.3?

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