A random sample is drawn from a normally distributed population with mean= 16 and standard deviation= 2.[You may find it useful to reference thez table.]

a.Are the sampling distribution of the sample mean withn= 24 andn= 48 normally distributed?

1. Yes, both the sample means will have a normal distribution.
2. No, both the sample means will not have a normal distribution.
3. No, only the sample mean with n = 24 will have a normal distribution.
4. No, only the sample mean with n = 48 will have a normal distribution.

b.Calculate the probabilities that the sample mean is less than 16.6 for both sample sizes.(Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)