Question

Part 1

A population of values has a normal distribution with μ=227.6μ=227.6 and σ=92.7σ=92.7. You intend to draw a random sample of size n=105n=105.

What is the mean of the distribution of sample means?
μ¯x= ______

What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σ¯x= ________

 

Part 2 

A population of values has a normal distribution with μ=244 and σ=18.6. You intend to draw a random sample of size n=178.

Find the probability that a sample of size n=178 is randomly selected with a mean between 241.8 and 244.4.
P(241.8 < M < 244.4) = _______

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