1. A country currently does not have a National Soccer League team. Fifty-two percent of all the residents are
in favor of attracting a soccer team. A random sample of 1200 residents is selected, and asked if they would
want a National Soccer team. What is the probability the percentage of those residents polled who are in favor
of attracting a soccer team is at least 60%? What does this probability mean in your own words? Is this what
you would have predicted? Why?
0.60 
x
1200

x  720
P( X  720)  P( Z  5.55)
 0.5  normalcdf (0, 5.55)
 0%
z
0.60  0.52
0.52(0.48)
1200

0.08
 5.56
0.0144
It is unlikely at least 60% of the residents are in favor of the team.
We could have predicted this because the z - score is so large.
2. How many people favor the Soccer League if we have a z – score of – 2.5?
 2.5 
pˆ  0.484
pˆ  0.52
 2.5 
0.52(0.48)
1200
pˆ 
x
n

0.484 
pˆ  0.52
0.0144
x
1200
 0.036  pˆ  0.52
x  580.8
 580 people favor the League
3. Suppose a water polo team has shown to win 68% of their matches. Assuming there are no ties, what is the
probability that they will win at least five of the remaining 11 season matches? What does this probability mean
in your own words?
P( X  5)  1  P( X  4)
 1  binomcdf (11, 0.68, 4)
 96.9%
It is highly likely that the team wins at least 5 matches.
4. What is the probability that the team wins seven matches? In your own words, what does this probability
mean?
P( X  7)  binompdf (11, 0.68, 7)
 23.3%
It is unlikely the team will win 7 matches.
5. What is the probability the team wins between five and nine matches, inclusive? In your own words, what
does this probability mean?
P(5  X  9)  binomcdf (11, 0.68, 9)  binomcdf (11, 0.68, 4)
 88%
It is likely that the team wins at least 5 matches but no more than 9.
6. A quality control department has determined an upgrade in equipment will be necessary if the mean number
of defective products is twelve with a standard deviation of three. If a sample of 34 factories is taken, find the
probability that the mean number of defects is less than eleven? In your own words, what does this probability
mean?
P( X  11)  P( Z  1.94)
 0.5  normalcdf (1.94, 0)
 2.6%
11  12
1
z

 1.94
3
0.5145
34
It is highly unlikely that the average number of defects will be less than 11.
7. What is the average number of defective products represented by the z – score 1.5?
1.5 
x  12
3
34
1.5 
0.77174  x  12
x  12
0.5145
x  12.77 defects
8. The following data represents the daily high temperatures for September in Tulare County. Make a sketch of
the distribution and comment on its shape.
77
85
82
88
82
85
79
85
80
85
80
86
81
88
81
85
82
86
82
87
83
87
83
87
86
88
92
92
Frequency
76
84
76
78
80
82
84
86
Temperature
88
90
92
94
The distribution appears to be normal.
9. What is the probability the temperature will be higher than 90? What does this probability mean in your own
words?
Using 1-Var Stats we get
and
x  84.13
s  3.83
90  84.13
z
 1.53
3.83
P(T  90)  P( Z  1.53)
 .5  normalcdf (0, 1.53)
 6.3%
It is unlikely the temperature will be higher than 90 in September.
10. What is the probability the temperature will be between 81 and 87? Is this probability what you would
have expected? Why?
z
81  84.13
 0.817
3.83
z
87  84.13
 0.749
3.83
P(81  T  87)  P(0.817  Z  0.749)
 56.6%
This probability matches the area shaded in our graph, so 56.6% seems like a reasonable percentage.