3. Assume the weights of adult male pygmy-possums in Australia are normally distributed with a mean of 8.5 g and a standard deviation of 0.3 g. (a) Identify the population and the variable. Population: Variable: (b) For samples of size four, find the mean ay and standard deviation o, of all possible sample mean weights. Mean of &: Standard Deviation of &: (c) Find the percentage of all samples of four pygmy-possums that have mean weights within 0.5 g of the population mean weight of 8.5 g. 4. Assume the serum cholesterol levels in men age 18-24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7. (Units are mg/100 ml., and the data are based on the National Health Survey.) (a) Suppose 64 men age 18-24 are randomly selected. Find the probability their mean serum cholesterol level is greater than 185. (b) If the serum cholesterol levels in men age 18-24 are not normally distributed, can you answer part (a)? Why or why not? (You must justify your answer to receive credit. Be specific.)