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 5.7 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 \(\mu_{X}=\sum_{i = 1}^{n}x_{i}p_{i}\), where \(x_{i}\) are the values of the random variable and \(p_{i}\) are the corresponding probabilities. First, find the total number of series \(N=20 + 22+22 + 32=96\). Then, the probabilities are \(p_{4}=\frac{20}{96}\), \(p_{5}=\frac{22}{96}\), \(p_{6}=\frac{22}{96}\), \(p_{7}=\frac{32}{96}\).

Step2: Calculate the mean

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The mean of a discrete random variable represents the long - run average value. If the experiment (in this case, the tournament series) is repeated many times, the average number of games per series is given by the mean.

Answer:

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