A random sample of size n = 58 is taken from a finite population of size N = 671 with mean = 252 and variance ² = 268. [You may find it useful to reference the z table.]

a-1. Is it necessary to apply the finite population correction factor?

multiple choice

• 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 final answer to 4 decimal places.)

c. What is the probability that the sample mean lies between 246 and 261? (Round final answer to 4 decimal places.)