Question

The following data represent the number of games played in each series of an annual tournament from 1924 to 2005.

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

x (games played)   Frequency
4   16
5   14
6   19
7   32

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

​(b) Graph the discrete probability distribution. Choose the correct graph below.

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

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

Answer 1

a) Discrete probability distribution for the random variable x :

X	P(X)
4	0.1975
5	0.1728
6	0.2346
7	0.3951
Total	1

b)

c)

X	P(X)	X.P(X)	X².P(X)
4	0.1975	0.7901	3.1605
5	0.1728	0.8642	4.3210
6	0.2346	1.4074	8.4444
7	0.3951	2.7654	19.3580
Total	1	5.8272	35.2840

Mean, μ = Ʃ[X.P(X)] = 5.8272

The series, if played many times, would be expected to last about 5.8272 games, on average.

d)

Standard deviation, σ = √[Ʃ(X².P(X)) - μ²] = √(35.2840 - 5.8272²) = 1.1525