Question 1 Assume that the weight of a typical male follows normal distribution with =180 lb and =30 lb, a) (5 points) What fraction of males weigh more than 210 pounds? b) (10 points) What is the range of weight values who are in the 80th percentile? Hint: Let us say the cutoff point (maximum value of weight) for 80th percentile is y. The value of y should satisfy P(Xy)=0.8.

Question 2 A production process manufactures items with weights that are normally distributed with mean 17 pounds and standard deviation 0.1 pound. An item is considered to be defective if its weight is less than 16.8 pounds or greater than 17.2 pounds. Suppose that these items are currently produced in batches of 500 units. a) (10 points) Find the probability that an inspected item is defective. b) (10 points) Find the probability that at most 4% of the items in a given batch will be defective. Hint: Find the probability that an item is defective using Normal probabilities. Then, you can model number of defectives out of 500 as Binomial.

Question 3 A sample of n=16 observations is drawn from a normal population with =1000 and =200. Find the following: a) (5 points) ( > 1070) b) (5 points) (990 < 1150)

Question 4 (15 points) Determine the probability that in a sample of 100 the sample proportion is less than 0.77 if p=0.8.

Question 5 Consider the following hypotheses: H0: 400, Ha: 400 Given that s=100, n=1000, = 405, =0.05, a) (5 points) Calculate the value of the test statistic. b) (5 points) Write a mathematical expression for the rejection region. c) (5 points) Determine the p-value. d) (5 points) Interpret the result.

Question 6 (20 points) A diet doctor claims that the average North American is more than 20 pounds overweight. To test his claim, a random sample of 20 North Americans was weighed, and the difference between their actual and ideal weights was calculated. The data are listed here. Do these data allow us to infer at the 5% significance level that the doctor's claim is true? 16 23 18 41 22 18 23 19 22 15

18 35 16 15 17 19 23 15 16 26