Question

The following data represent the number of games played in each series of an annual tournament from

1923 to 2001.

Complete parts​ (a) through​ (d) below.

x​ (games played)	4	5	6	7	Copy to Clipboard + Open in Excel +
Frequency	17	14	22	25

​(a) Construct a discrete probability distribution for the random variable x.

x​ (games played)	​P(x)
4
5
6
7

​(Round to four decimal places as​ needed.)

​​(c) Compute and interpret the mean of the random variable x.

​(Round to four decimal places as​ needed.)

Interpret the mean of the random variable x.

The​ series, if played many​ times, would be expected to last about 4.3 ​games, on average.

B. The​ series, if played one​ time, would be expected to last about 5.7 games.

C. The​ series, if played many​ times, would be expected to last about 5.7 ​games, on average.

​(d) Compute the standard deviation of the random variable x.

​(Round to one decimal place as​ needed.)

Answer 1

a) Total frequency = 17 + 14 + 22 + 25 = 78

x                P(x)

4                17 / 78 = 0.2179

5                14 / 78 = 0.1795

6                22 / 78 = 0.2821

7                25 / 78 = 0.3205

c) Mean = E(X) = 4 * 0.2179 + 5 * 0.1795 + 6 * 0.2821 + 7 * 0.3205 = 5.7052

Option-C) The​ series, if played many​ times, would be expected to last about 5.7 ​games, on average.

d) E(X²) = 4² * 0.2179 + 5² * 0.1795 + 6² * 0.2821 + 7² * 0.3205 = 33.834

Var(X) = E(X²) - (E(X))² = 33.834 - 5.7052² = 1.2847

SD(X) = sqrt(1.2847) = 1.1