Suppose X follows a normal distribution with mean1 and varia

Suppose X follows a normal distribution with mean=1 and variance=4. Let\'s randomly select 4 numbers from X. What is the distribution of the mean of these four numbers? What is the probability that the mean is between -1 and 1?

Solution

The distribution of mean is also normal distribution with mean 1 and variance 1

Probability that the mean is between -1 and 1 is 0.47725