Question

The following data represent the number of games played in each series of an annual tournament from

19331933

to

20022002.

Complete parts? (a) through? (d) below.

x? (games played)

4

5

6

7

	Copy to Clipboard			+
	Open in Excel			+

Frequency

1717

1515

2121

1616

?(a) Construct a discrete probability distribution for the random variable x.

x? (games played)	?P(x)
4	nothing
5	nothing
6	nothing
7	nothing

?(Round to four decimal places as? needed.)

?(b) Graph the discrete probability distribution. Choose the correct graph below.

A.

456700.5xP(x)

Edit Coordinates(0,0)

A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.35; 5, 0.22; 6, 0.4; 7, 0.23.

B.

456700.5xP(x)

Edit Coordinates(0,0)

A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.25; 5, 0.22; 6, 0.3; 7, 0.23.

C.

456700.5xP(x)

Edit Coordinates(0,0)

A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical line are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.35; 5, 0.32; 6, 0.4; 7, 0.33.

D.

456700.5xP(x)

Edit Coordinates(0,0)

A histogram with a horizontal x-axis labeled from 3 to 8 in intervals of 1 and a vertical axis labeled "P(x)" from 0 to 0.5 in intervals of 0.1 has four vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 4, 0.15; 5, 0.12; 6, 0.2; 7, 0.13.

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

mu Subscript x?xequals=nothing

games

?(Round to four decimal places as? needed.)

Interpret the mean of the random variable x.

A.

The? series, if played many? times, would be expected to last about

5.55.5

?games, on average.

B.

The? series, if played one? time, would be expected to last about

5.55.5

games.

C.

The? series, if played many? times, would be expected to last about

4.54.5

?games, on average.

?(d) Compute the standard deviation of the random variable x.

sigma Subscript x?xequals=nothing

games

Answer 1

(a)

Following table shows the relative frequency distribution:

X	Frequency, f	P(X=x)=f/69
4	17	0.2464
5	15	0.2174
6	21	0.3043
7	16	0.2319
Total	69	1

(b)

Following table shows the histogram:

(c)

Following table shows the calculations for mean:

X	Frequency, f	P(X=x)=f/69	xP(X=x)
4	17	0.2464	0.9856
5	15	0.2174	1.087
6	21	0.3043	1.8258
7	16	0.2319	1.6233
Total	69	1	5.5217

So,

A.

The? series, if played many times, would be expected to last about 5.5 games, on average.

(d)

Following table shows the calculations:

X	Frequency, f	P(X=x)=f/69	xP(X=x)	x^2P(X=x)
4	17	0.2464	0.9856	3.9424
5	15	0.2174	1.087	5.435
6	21	0.3043	1.8258	10.9548
7	16	0.2319	1.6233	11.3631
Total	69	1	5.5217	31.6953

Answer: 32