Problem 1. Which one of the following charts represents a probability distribution (5 points): Problem 2. The number of crimes committed daily has some unknown probability distribution with the mean u = 2.8 and the standard deviation 5 = 4. A random sample of n = 100 days will be taken. Describe the distribution of the average number (the mean number) of crimes for that sample (5 points): a.) unknown distribution with the mean = 2.8 and the standard deviation = 0.4 b.) approximately normal distribution with the mean = 2.8 and the standard deviation = 4 C.) unknown distribution with the mean = 2.8 and the standard deviation = 4 d.) approximately normal distribution with the mean = 2.8 and the standard deviation = 0.4 Problem 3. From the table below, find Prof. Aker's expected mean lateness. (5 points) P Lateness 4/5 1/10 1/20 1120 Problem 4. There are 7 different restaurants in the X City. Part a. You want to choose 2 different restaurants from them. In how many different ways can you do that? (5 points) Part b. You want to choose two different restaurants to eat your lunch in the first one of them and your dinner in the second one of them. In how many different ways can you do that? (5 points) Part c. You want to choose two restaurants to eat your lunch in the first one of them and your dinner in the second one of them. The restaurants do not have to be different - you are OK to eat lunch and dinner in the same restaurant. In how many different ways can you do that? (5 points) Problem 5. In a box there are 9 red balls and 4 green balls. Part a. Two random balls are taken one-after-another from that box, with replacements (which means that each taken ball is instantaneously replaced by an identical ball). What is the probability that both of these balls are red? (5 points) Part b. Two random balls are taken from that box without replacements (which means that what is taken is gone). What is the probability that both of these balls are red? (5 points) Problem 6. Three hundred viewers were asked if they are satisfied with the TV coverage of a recent disaster. We are given the following table: -EE_ TOTAL Satisfied TOTAL Not Satisfied A viewer was randomly selected from those surveyed. Part a. Find the probability that this viewer is satisfied. (5 points) Part b. Find the probability that this viewer is a female or that this viewer is not satisfied. (5 points) Part c. Find the probability that this viewer is satisfied if you are told that this viewer is male. (5 points) Problem 7. According to the National Health Survey, American men's heights are normally distributed with the mean .u = 69.7 inches and the standard deviation 0 = 2.8 inches. Part a. A man is randomly selected. Find the probability that his height is more than 72 inches. (5 points) Part b. A man is randomly selected. Find the probability that his height is between 68 and 72 inches. (5 points) Problem 8. The amount of a popular drink in bottles has the normal distribution with the mean ,u = 101.5 milliliters (mL) and the standard deviation 0 = 1.6 milliliters (mL). If n = 36 bottles are randomly selected, find the probability that the average content in these selected bottles is smaller than 102.1 milliliters (mL). (15 points) Problem 9. One in every three Americans believes that the U.S government should send a mission to Mars. If n = 30 Americans are randomly selected, find the probability that Part a. Exactly 8 out of these 30 selected Americans believe that the U.S government should send a mission to Mars. (10 points) Part b. At least 8 out of these 30 selected Americans believe that the U.S government should send a mission to Mars. (5 points. No need to show calculations you can use software) Part c. Use the Normal Distribution to find the approximate answer in Part b. (5 points)