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 


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 xaxis 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 xaxis 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 xaxis 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 xaxis 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
(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
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