Suppose that weights of American adult males is Normally distributed with mean 165 pounds and standard deviation 15 pounds. A random sample of 36 adult American males is obtained.
1. Determine the mean of the sampling distribution of the sample mean, i.e., the mean of the distribution of possible values of the sample mean (x-bar)
2. Determine the standard deviation of the sampling distribution of the sample mean (also called the standard error of x-bar), i.e., the standard deviation of the distribution of possible values of the sample mean (x-bar)
3. Describe the shape, if possible, of the sampling distribution of the possible values of the sample mean (X-bar). If not possible, explain why
4. Find the probability that a single randomly selected adult American Male will weigh more than 170 pound
5. Find the probability that the mean weight of 36 randomly selected adult American males exceeds 170 pounds.