A random sample of size n = 64 is obtained from a normally distributed population with a population mean = 80 and variance 2 = 25.

a) What are the mean and standard deviation of the sampling distribution for the sample means?

b) What is the value of the sample variance such that 5% of the sample variances would be less than this value? ( hint: You can use interpolation or taking averages of the critical chi-squared values if you need to)

c) What is the value of the sample variance such that 10% of the sample variances would be greater than this value?