A normal population has known mean = 50 and variance 2 = 5. What is the approximate

Question:

A normal population has known mean μ = 50 and variance σ2 = 5. What is the approximate probability that the sample variance is greater than or equal to 7.44? less than or equal to 2.56?
(a) For a random sample of n = 16.
(b) For a random sample of n = 30.
(c) For a random sample of n = 71.
(d) Compare your answers to parts (a)–(c) for the approximate probability that the sample variance is greater than or equal to 7.44. Explain why this tail probability is increasing or decreasing with increased sample size.
(e) Compare your answers to parts (a)–(c) for the approximate probability that the sample variance is less than or equal to 2.56. Explain why this tail probability is increasing or decreasing with increased sample size.