Question 6,6.1.19

Part 8 of 8

HW Score:53.23%, 11.18 of 21 points

Points:0.85 of 1

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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

0.1662

1

0.3365

2

0.2872

3

0.1485

4

0.0384

5

0.0232

(a) Verify that this is a discrete probability distribution.

This is a discrete probability distribution because all of the probabilities are

between

0

0 and

1

1, inclusive, and the sum

of the probabilities is

1

1.

(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.

A.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

NumberofHits

Probability

The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.02; 1, 0.04; 2, 0.15; 3, 0.29; 4, 0.34; 5, 0.17.

B.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

NumberofHits

Probability

The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.15; 1, 0.04; 2, 0.02; 3, 0.17; 4, 0.34; 5, 0.29.

C.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

NumberofHits

Probability

The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0.34; 1, 0.15; 2, 0.02; 3, 0.17; 4, 0.29; 5, 0.04.

D.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

NumberofHits

Probability

The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.17; 1, 0.34; 2, 0.29; 3, 0.15; 4, 0.04; 5, 0.02.

Your answer is correct.

Describe the shape of the distribution.

The distribution has one mode

and is skewed right.

(c) Compute and interpret the mean of the random variable X.

X=

1.626

1.626 hits

(Type 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.

In any number ofgames, one would expect the mean number of hits per game to be the mean of the random variable.

C.

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

Your answer is correct.

D.

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

(d) Compute the standard deviation of the random variable X.

X= ___________ hits