A probability distribution has a mean of 50 and a standard deviation of 15. We plan to take a sample of 35 observations. What is the probability that the sample mean is between 48 and 54? Select one: O a. 0.1577 O b. 0.4911 O C 0.7281 O d. 0.2852A probability distribution has a mean of 32 and a standard deviation of 6. We plan to take a sample of 40 observations. What is the z-value at the sample mean of 35? Select one: O a, 0.50 O b. 1.28 OC -3.16 O d. 3.16A probability distribution has a mean of 50 and a standard deviation of 15. We plan to take a sample of 35 observations. What is the probability that the sample mean is between 48 and 50? Select one: O a. 0.4500 O b. 0.2852 O C. 0.7852 O d. 0.2148