Question

in the probability distribution to the right, the random variable x represents the number of hits a baseball player obtained in a game over the course of a season. complete parts (a) through (f) below.
which of the following interpretations of the mean is correct?
a. the observed number of hits per game will be less than the mean number of hits per game for most games.
b. the observed number of hits per game will be equal to the mean number of hits per game for most games.
c. in any number of games, one would expect the mean number of hits per game to be the mean of the random variable.
d. over the course of many games, one would expect the mean number of hits per game to be the mean of the random variable.
(d) compute the standard deviation of the random variable x.
σx = □ hits
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the mean ($\mu$)

The formula for the mean of a discrete random variable is $\mu=\sum_{x}x\cdot P(x)$.

$$
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$$

Step2: Calculate $E(X^{2})=\sum_{x}x^{2}\cdot P(x)$

$$
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$$

Step3: Calculate the variance ($\sigma^{2}$)

The formula for the variance is $\sigma^{2}=E(X^{2})-\mu^{2}$.

$$
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$$

Step4: Calculate the standard deviation ($\sigma$)

The formula for the standard deviation is $\sigma=\sqrt{\sigma^{2}}$.

$$ \sigma=\sqrt{1.2835}\approx1.133 $$

Answer:

$1.133$