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 game(s).

(d) compute the standard deviation of the random variable ( x ).
( sigma_{x}=square ) game(s)
(round to one decimal place as needed.)

Explanation:

Step1: Calculate the total number of series

The total number of series \( n=\sum f = 20 + 22+22 + 32=96\)

Step2: Calculate the expected value \(E(X)\) (already given as \(\mu_X = 5.7\))

Step3: Calculate \(E(X^{2})\)

$$
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$$

Step4: Calculate the variance \(\sigma_{X}^{2}\)

$$
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$$

Step5: Calculate the standard deviation \(\sigma_{X}\)

$$ \sigma_{X}=\sqrt{\sigma_{X}^{2}}=\sqrt{1.11}\approx1.0 $$

Answer:

\(\sigma_{X}\approx1.0\) game(s)