A random sample of size n = 85 is taken from a finite population of size N = 479 with mean μ = 253 and variance σ2 = 436. [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.(Round “expected value” to a whole number and "standard error" to 4 decimal places.)

b. What is the probability that the sample mean is less than 241? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What is the probability that the sample mean lies between 246 and 262? (Use rounded standard deviation. Round "z" value to 2 decimal places and final answer to 4 decimal places.)