A random sample of size n = 50 is taken from a population with mean = 9.5 and standard deviation = 2. [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 deviation" to 4 decimal places.)

b. What is the probability that the sample mean is less than 10? (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 10 and 9? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)