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 0.41. Which one of the following charts represents a probability distribution (5 points):| a) X P(x) 0 -0.1 + 1 0.1 2 0.4 3 0.6 ent will b) X P(x) 0 0.3 1 0.2 2 0.1 3 0.35 C X P(x) 0 0.1 0.2 2 0.4 3 0.1 d) X P(x) 0 0 2 3 02 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 1/205. 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. (10 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.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) x P(x) 0 0.10 0.16 2 a 3 0.31 4 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.