The following data represent the number of games played in each series of an annual tournament from 1926 to 2006. x (games played) 4 5 6 79 Frequency 19 16 15 30 (a) Construct a discrete probability distribution for the random variable X, P (x;) = N. x (games played) P(x) 5 6 (Round to four decimal places as needed.) (b) Draw the probability histogram. Choose the correct histogram below. A. OB O C. OD. AP ( x ) 0.5 Q AP(X) 0.5 AP ( x) AP( x) 0.5 0.5 Q 8 8 (c) Compute the mean of the random variable X. Hx =games (Round to four decimal places as needed.) Interpret the mean of the random variable X. O A. The series, if played many times, would be expected to last about 5.7 games, on average. O B. The series, if played one time, would be expected to last about 5.7 games. O C. The series, if played many times, would be expected to last about 4.3 games, on average. (d) Compute the standard deviation of the random variable X. ox = games (Round to the nearest tenth as needed.) Time Remaining: 01:56:In the following probability distribution, the random variable X represents the number of activities a parent of a K to 5th-grade student is involved in. Complete parts (a) through (f) below. X 0 1 2 3 4 P(x) 0.304 0.144 0.236 0.095 0.221 (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) Draw a probability histogram. Choose the correct graph below. O A. OB O c. O D. 0.5- 0.5- 0.5 0.5 Q 0.4- 0.4- 0.4- 0.4- 0.3- 0.3- 10.3- 0.3- 0.2- 0.2- 0.1- 10.2- 012 3 (c) Compute and interpret the mean of the random variable X The mean is activities. (Round to one decimal place as needed.) Which of the following interpretations of the mean is correct? O A. The observed value of an experiment will be less than the mean of the random variable in most experiments. O B. The observed value of an experiment will be equal to the mean of the random variable in most experiments. O C. As the number of experiments decreases, the mean of the observations will approach the mean of the random variable. O D. As the number of experiments increases, the mean of the observations will approach the mean of the random variable. (d) Compute the standard deviation of the random variable X. The standard deviation is |activities. (Round to one decimal place as needed.) (e) What is the probability that a randomly selected student has a parent involved in three activities? The probability is (Type an integer or a decimal.) (f) What is the probability that a randomly selected student has a parent involved in three or four activities? The probability is. (Type an integer or a decimal.) Time Remaining: 01:55:37 Nexpossible Calculate the correlation coefficient for the following ordered pairs. 5 2 3 9 11 8 r= (Round to three decimal places as needed.)