Question

the following data represent the number of games played in each series of an annual tournament from 1923 to 2019. complete parts (a) through (d) below

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

\\( \mu _ { x } = 5.7 \\) game(s)

(round to one decimal place as needed.)

interpret the mean of the random variable x. select the correct choice below and fill in the answer box within your choice.

(round to one decimal place as needed.)

a. the series, if played many times, would be expected to last about \\( \square \\) game(s), on average.

b. the series, if played one time, would be expected to last about \\( \square \\) game(s).

Explanation:

Step1: Recall the formula for the mean of a discrete random variable

The formula for the mean \(\mu_X=\sum_{i}x_ip_i\). First, we need to find the total number of series \(n = 20 + 22+22 + 32=96\). Then, the probability \(p_i=\frac{\text{Frequency}_i}{n}\).

Step2: Calculate the mean

$$
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The mean of a random variable represents the long - term average value. So, if the series is played many times, we use the concept of the expected value (mean of the random variable).

Answer:

A. The series, if played many times, would be expected to last about \(5.7\) game(s), on average.