Assume that the data in the first histogram represents the heights of American males, and suppose these are normally distributed with mean of 69 inches and a standard deviation of 4 inches.

1. What is the probability that a randomly picked American male is shorter than 65 inches?

2. What is the probability that the mean height of a random sample of 10 American males is between 68 inches and 70 inches?

3. Suppose that the data going into the mean and standard deviation quoted above is actually from a random sample of size 36. Construct a 95% confidence interval for the population mean height of adult males.

4. Explain the interpretation of the confidence interval (one-sentence).

5. Based on your answers to parts c & d, would a hypothesis test of whether the population means was equal to 72 be statistically significant at alpha=.05? Why or why not? (One sentence answer: please don't actually do a test!)