Question

in the given probability distribution, 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).

μx = 1.6267 hits
(type an integer or a decimal. do not round.)

which of the following interpretations of the mean is correct?

oa. in any number of games, one would expect the mean number of hits per game to be the mean of the random variable.

ob. the observed number of hits per game will be less than the mean number of hits per game for most games.

oc. over the course of many games, one would expect the mean number of hits per game to be the mean of the random variable.

od. the observed number of hits per game will be equal to the mean number of hits per game for most games.

Explanation:

The mean of a probability distribution represents the long - term average. It is not about individual games or a small number of games. Option A is incorrect because it says "in any number of games" instead of a large number. Option B is wrong as there's no guarantee that the observed number is less than the mean for most games. Option D is incorrect because the observed number is not equal to the mean for most games. Option C is correct as it refers to the long - term (over many games) average which is the essence of the mean of a probability distribution.

Answer:

C. Over the course of many games, one would expect the mean number of hits per game to be the mean of the random variable.