A random sample of size n = 178 is taken from a population of size N = 3,718 with mean μ = −80 and variance σ2 = 190. [You may find it useful to reference the z table.]   a-1. Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)   b. What is the probability that the sample mean is between −82 and −78? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)   c. What is the probability that the sample mean is greater than −79? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

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