3. AB? is studying the consumption of electricity indifferent households in Ohio. Let Y denote the consumption of electricity. The researchers mode] the consumption as a normal distribution and sample n. = 16 households. Let Y denote the sample mean and let s denote the sample standard deviation. Answer the following questions. (If the exact values you need to solve these problems are not available in the appropriate table, use the closest values that are available.) (a) Assume that the population mean consumption is ,u = 30 but that the population standard deviation is unknown. The calculated sample standard deviation is s = 5. What is the (ap- proximate) probability that the sample mean is within 2.5 units of the population mean? (5 as) (b) Assume that the population mean consumption is / = 30 and the population standard deviation is known to be o = 5.30. What is the probability that the sample standard deviation s is greater than 4? (5 pts)