1. Which one of the following charts represents a probability distribution (5 points): a) b) c) d) X P(x) X P(x) X P(x) X P(x) 0 0.1 0 0 0.1 0.3 0.2 0.1 0.2 2 0.4 2 2 0.4 2 0.1 3 0.1 3 3 0.6 3 0.35 2. The number of violent crimes committed in a day possesses a distribution with a mean of 2.8 crimes per day and a standard deviation of 4 crimes per day. A random sample of 100 days was observed, and the sample mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample means. (5 points) a.) shape unknown with mean of 2.8 and a standard deviation of 0.4 b.) approximately normal with mean of 2.8 and standard deviation of 4 c.) shape unknown with mean of 2.8 and standard deviation of 4 d.) approximately normal with mean of 2.8 and standard deviation of 0. 3. From the table below, find Prof. Xin expected value of lateness. (5 points) Lateness P(Lateness) On Time 4/5 1 Hour Late 1/10 2 Hours Late 1/20 3 Hours Late 1/204. Suppose Ches Tahoe restaurant is one of the 7 largest restaurants in X City. a. You would like to choose two different restaurants from them. How many different ways are there? (5 points) b. You would like to choose two different restaurants. One is for your lunch and the other one is for your dinner. How many different ways are there? (5 points) c. You would like to choose two restaurants. One is for your lunch and the other one is for your dinner. You are OK for going to the same restaurants. How many different ways are there? (5 points) 1. Suppose that 9 good fuses and 4 defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random. What is the probability that we are lucky and find both of the defective fuses in the first two tests? (5 points) 1). With replacement 2). Without replacement6. Three hundred viewers were asked if they were satisfied with TV coverage of a recent disaster. (15 points) Female (F) Male (M) TOTAL Satisfied (S) 80 55 Not Satisfied (N) 120 45 TOTAL If a viewer is to be randomly selected from those surveyed. a) Find the probability that the viewer is satisfied. b) Find the probability that the viewer is a female or the viewer is not satisfied. c) Find the probability that the viewer is satisfied given that the viewer is male.7. According to a National Health Survey, American men's heights are normally distributed with a mean given by # = 69.7 inches and a standard deviation given by 0 = 2.8 inches. a). If a man is randomly selected, find the probability that his height is more 72 inches. (5 pints) b). If a man is randomly selected, find the probability that his height is between 68 and 72 inches. (10 points)8. Suppose the amount of a popular sport drink in bottles leaving the filling machine has a normal distribution with mean 101.5 milliliters (mL) and standard deviation 1.6. If 36 bottles are randomly selected, find the probability that the mean content is less than 102.1 mL (10 points) 9. One out of every three Americans believes that the U.S government should take "primary responsibility" for eliminating poverty in the United States. If 30 Americans are selected, find the probability that a) Exactly eight (8) will believe that the U.S government should take "primary responsibility" for eliminating poverty. (10 points)9. One out of every three Americans believes that the U.S government should take "primary responsibility" for eliminating poverty in the United States. If 30 Americans are selected, find the probability that a) Exactly eight (8) will believe that the U.S government should take "primary responsibility" for eliminating poverty. (10 points) b) At least eight (8) will believe that the U.S government should take "primary responsibility" for eliminating poverty. (5 points, calculation is not necessary) 6 c) Use Normal Distribution for part b). (10 points)