A random sample is drawn from a normally distributed population with mean = 35 and standard deviation = 2.3. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 43 and n = 86 normally distributed?

multiple choice

• 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 = 43 will have a normal distribution.
• No, only the sample mean with n = 86 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 35.8 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.)

43

86