A random sample of size n = 82 is taken from a population with mean = 15.6 and standard deviation = 5. [You may find it useful to reference the z table.]

a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard error" to 4 decimal places.)

b. What is the probability that the sample mean is less than 16?(Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

c. What is the probability that the sample mean falls between 16 and 15? (Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to 4 decimal places.)