In the following probability distribution, the random variable x represents the number of activities a parent of a 6th- to 8th-grade student is involved in. Complete parts (a) through (f) below. to 1 2 3 4 P(x) 0.406 0.137 0.108 0.158 0.191 ... (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because the sum of the probabilities is and each probability is (b) Graph the discrete probability distribution. Choose the correct graph below. O A. В. о в. OC. O D. 0.5- 0.57 0.5- 0.57 0.4- 0.4- 0.4- 0.4- 0.3- 0.2- 0.3- 0.3- 0.3- 0.2- 0.2- 0.2- 田 0.1- 0.1+ 0.1- 0.1- 0-

A student needs to know details of a class assignment that is due the next day and decides to call fellow class members for this information. She believes that for any particular call, the probability of obtaining the necessary information is 0.40. She decides to continue calling class members until the information is obtained. But her cell phone battery will not allow more than 8 calls. Let the random variable X denote the number of calls needed to obtain the information.a. Find the probability distribution of X.b. Find the cumulative probability distribution of X.c. Find the probability that at least three calls are required.

In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal.t You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent nine shark attacks, all of which were nonfatal. Let r be the number of nonfatal attacks out of a random sample of nine shark attacks. In USE SALT (a) Make a histogram for the probability distribution of r. 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 P(r) P(r) P(r)

In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal.t You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent six shark attacks, all of which were nonfatal. Let r be the number of nonfatal attacks out of a random sample of six shark attacks. (a) Make a histogram for the probability distribution of r. 0.35 0.35 0.30 0.30 0.25 0.25 3 0.20 * 0.20 0.15 0.15 0.10 0.10 0.05 0.05 3 6. 2 4 0.35 0.35 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.10 0.10 0.05 0.05 3 6. 3 6. (b) What is the probability all six shark attacks are nonfatal? (Round your answer to three decimal places.) (c) What is the probability that three or more of the six shark attacks are nonfatal? (Round your answer to three decimal places.) (d) What is the expected number of nonfatal shark attacks out of the six? What is the standard deviation of the r-probability distribution? (Round your…