A random sample is drawn from a normally distributed population with mean ? = 31 and standard deviation ? = 1.9. [You may find it useful to reference the z table.]a. Are the sampling distribution of the sample mean with n = 39 and n = 76 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 = 39 will have a normal distribution. No, only the sample mean with n = 76 will have a normal distribution.b. Calculate the probabilities that the sample mean is less than 31.6 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.)

A random sample is drawn from a normally distributed population with mean // = 31 and standard deviation q = 1.9. [You may find it useful to reference the z table.] a. Are the sampling distribution of the sample mean with n = 39 and n = 76 normally distributed? Yes, both the sample means will have a normal distribution. O No, both the sample means will not have a normal distribution. O No, only the sample mean with n = 39 will have a normal distribution. O No, only the sample mean with n = 76 will have a normal distribution. b. Calculate the probabilities that the sample mean is less than 31.6 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, "2" value to 2 decimal places, and final answer to 4 decimal places.) n Probability 39 76