Question

The following data represent the number of games played in each series of an annual tournament from 1924 to 2002. Complete parts​ (a) through​ (d) below. x​ (games played) 4 5 6 7 Frequency 19 17 20 22 ​(a) Construct a discrete probability distribution for the random variable x. x​ (games played) ​P(x) 4 nothing 5 nothing 6 nothing 7 nothing ​(Round to four decimal places as​ needed.) ​(b) Graph the discrete probability distribution. Choose the correct graph below. A. 4 5 6 7 0 0.5 x P(x) A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.24; 5, 0.22; 6, 0.26; 7, 0.28. B. 4 5 6 7 0 0.5 x P(x) A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.34; 5, 0.22; 6, 0.36; 7, 0.28. C. 4 5 6 7 0 0.5 x P(x) A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.14; 5, 0.12; 6, 0.16; 7, 0.18. D. 4 5 6 7 0 0.5 x P(x) A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical line are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.34; 5, 0.32; 6, 0.36; 7, 0.38. ​(c) Compute and interpret the mean of the random variable x. mu Subscript xequals nothing games ​(Round to four decimal places as​ needed.) Interpret the mean of the random variable x. A. The​ series, if played many​ times, would be expected to last about 5.6 ​games, on average. B. The​ series, if played one​ time, would be expected to last about 5.6 games. C. The​ series, if played many​ times, would be expected to last about 4.4 ​games, on average. ​(d) Compute the standard deviation of the random variable x. sigma Subscript xequals nothing games ​(Round to one decimal place as​ needed.)

Answer 1

1. X:       4                5              6              7

P(x) .24                .22          .26          .28

2. First option is correct
3. E(X)= 5.576923=5.6(approx. to one decimal) ,

Correct option is

A. The​ series, if played many​ times, would be expected to last about 5.6 ​games, on average.

d) SD= 1.138143=1.1(approx to one decimal)