SOLUTION: A random sample is drawn from a population with mean μ = 55 and standard deviation σ = 4.6. [You may find it useful to reference the z table.] a. Is the sampling distribu

Question 1162759: A random sample is drawn from a population with mean μ = 55 and standard deviation σ = 4.6. [You may find it useful to reference the z table.]

a. Is the sampling distribution of the sample mean with n = 13 and n = 37 normally distributed?

Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal distribution.
No, only the sample mean with n = 13 will have a normal distribution.
No, only the sample mean with n = 37 will have a normal distribution.

b. Calculate the probability that the sample mean falls between 55 and 57 for n = 37. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If the population is normally distributed, then the sampling distribution of both will be normal.
If the population is not normally distributed, then it depends.
Because the z-table is being used, and because sigma and not s is used, I would assume normality in the population and the answer is Yes.
z=(57-55)/4.6/sqrt(37)
=2*sqrt(37)/4.6=2.64
So between 55 (z=0) and 57 (z=2.6446) that probability is 0.4959

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