In the probability distribution to theright, 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.

X P(x)

0 0.1686

1 0.3343

2 0.2863

3 0.1496

4 0.0363

5 0.0249

A) Verify that this is a discrete probability distribution.

This is a discrete probability distribution because ______(at least one of the probabilities is or all of the probabilities are) between ___ and ____ inclusive, and the ___ (mean, sum or product) of the probabilities is____.

(Type whole numbers. Use ascendingorder.)

B) Draw a graph of the probability distribution. Describe the shape of the distribution.

Graph the probability distribution. Choose the correct graph below.

The distribution ____ (is multimodal, has one mode, is uniform, or is bimodal) and is ____ (skewed right, roughly symmetric, or skewed left).

C) Compute and interpret the mean of the random variable X.

X= ____ hits

(an integer or a decimal. Do notround.)

Which of the following interpretations of the mean iscorrect?

A.

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

B.

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

C.

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

D.

In any number ofgames, 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.

X=_____ hits

(Round to three decimal places asneeded.)

E) What is the probability that in a randomly selectedgame, the player got 2hits?

_____

( an integer or a decimal. Do notround.)

F) What is the probability that in a randomly selectedgame, the player got more than 1hit?

______

(an integer or a decimal. Do notround.)