1. Which one of the following charts represents a probability distribution (5 points): a) (0) P(x) 10.2 2 0.4 0.1 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 1/20 4. A small start up tech company has 4 customer service telephone lines. Let xdenote the number of phone lines in use at any given time. Suppose that the probability distribution of x is as follows: (10 points) P(x) 0 0.10 0.16 0.31 0.22 a.) Determine the value of a if the data above represent a discrete probability distribution. b.) Calculate and interpret the expected value of x. c.) Calculate the standard deviation of x. 3. A history lecture hall class has 15 students. There is a 15% absentee rate per class meeting a.) Find the probability that exactly one student will be absent from class. (5 points) b) Find the probability that at least 2 students will be absent from class. (10 points) 6. Three hundred viewers were asked if they were satisfied with TV coverage of a recent disaster. (15 points) TOTAL Female (F) 80 120 Satisfied (S) Not Satisfied (N) TOTAL 5 Male (M) 5 45 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. 6. Find P(Z > -1.50) (5 points) 7. According to a National Health Survey, American men's heights are normally distributed with a mean given by u = 69.7 inches and a standard deviation given by = 2.8 inches. a). If a man is randomly selected, find the probability that his height is more 72 inches. (10 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)