Download Statistics - Harrison High School

CCGPS ADVANCED ALGEBRA
Unit 1 Review
Name _________________________
1. There are four children in a room, ages ten, eleven, twelve, and fourteen. If a thirteen- year-old
child enters the room the
a)
b)
c)
d)
mean age and standard deviation will stay the same
mean age and standard deviation will decrease
mean age will increase and the standard deviation will decrease.
mean age will decrease and the standard deviation will increase.
2. In the accompanying display, which has the larger mean and which has the larger standard
deviation?
(a) Larger mean, A; larger standard deviation, A
(b) Larger mean, A; larger standard deviation, B
(c) Larger mean, B; larger standard deviation, A
(d) Larger mean, B; larger standard deviation, B
3. Jim made a 91 on an exam where the class grades were normally distributed with an average of
84 and a standard deviation of 5.2. Which is true about Jim’s score in relation to the rest of
the class?
(a) Jim’s score was 1.3 standard deviations below the mean
(b) Jim’s score was 1.3 standard deviations above the mean
(c) Jim’s score was above the 98th percentile of class scores
(d) Jim’s score was below the 84th percentile of class scores
4. Mrs. Reid’s math class had an average of 88 on the first test with a standard deviation of 3.2.
Ms. Nash’s math class had an average of 88 on the first test with a standard deviation of
5.1. Which is true in comparing the performance of the two classes?
(a) Both classes did equally well
(b) Ms. Nash’s class did worse than Mrs. Reid’s class
(c) Ms. Nash’s class had less variability in scores than Mrs. Reid’s class
(d) Ms. Nash’s class had more variability in scores than Mrs. Reid’s class
5. The five-number summary of a set of data is
A)
B)
C)
D)
The mean, standard deviation, first quartile, median, and third quartile.
The mean, median, mode, variance, and standard deviation.
The minimum, first quartile, median, third quartile, and maximum.
The minimum, first quartile, variance, third quartile, and maximum.
6. You are interested in finding out if students at your school think that fine arts programs
are receiving enough funding. You decide to use a written survey that you give to people
sitting at your regular lunch table. This is an example of:
A)
B)
C)
D)
self-selected sampling
convenience sampling
systematic sampling
random sampling
Free Response.
7. The standard deviation of 30 measurements of people’s weights (in pounds) is computed to
be 3.5. The variance of these measurements is:
8. Calculate the mean, median, mode, standard deviation, variance and range for the following data
10
21
13
19
21
14
Mean: __________
Median: _________
10
8
15
9
Mode: __________
Standard Deviation: ___________
Variance: ___________
Range: ___________
9. Calculate the mean, median, mode, standard deviation,variance, and range for the following
data set. (round to the nearest tenth)
Scores from the last test: 61
80
92
Mean: __________
Median: _________
99
78
90
95
41
75
68
Mode: __________
Standard Deviation: ___________
Variance: ___________
Range: ___________
10. Hotel occupancy rates often dictate how easy it might be to reserve a room at the last minute
and determine the average cost of a room. Rooms are often discounted in areas with low
occupancy. Occupancy rates across the United States for major cities are given below:
62
63
64
61
39
45
48
76
51
78
54
84
78
83
68
86
92
82
82
65
81
66
67
72
a) Compute the five-number summary.
b) Make a boxplot.
c) What scores separate the middle 50% of the data?
d) What scores separate the middle 68% of the data?
11. Class averages for 20 Math 2 sophomores are listed below.
98
97
89
93
79
88
81
82
80
65
90
89
80
80
81
70
a) Compute the five-number summary and the interquartile range.
b) Make a boxplot.
c) What scores separate the middle 50% of the data?
82
83
83
84
58
81
86
48
12. The class average on a math test was 68 and the standard deviation was 3.6. Find the zscore for a test score of 56. What kind of conclusion can you make about this students’
test score?
13. Lewis earned 85 on his health midterm and 82 on his math midterm. In the health class the
mean score was 79 with a standard deviation of 2. In the math class the mean score was 84
with a standard deviation of 4.
(a) Convert each score to a standard z score.
(b) On which test did he do better compared to the rest of the class?
14. A student scores 625 on the mathematics section of the SAT and a 28 on the mathematics
section of the ACT. She can report only one score to her college. If the SAT has a mean of 490
and a standard deviation of 100 and the ACT has a mean of 21 and a standard deviation of 6,
which score should she report?
15. The heights (in inches) of Ms. Larson’s 6th grade social studies class is given in the data set
below.
48, 61, 55, 51, 50, 46, 52, 61
a) What is the mean and standard deviation of these heights?
b) Draw and label a normal curve (with percentages) for the heights of the 6th graders.
c) What scores separate the middle 68% of the data?
16. The scores on a university examination are normally distributed with a mean of 74 and a
standard deviation of 9. If the middle 68% of students will get a “C”, what is the highest mark that a
student can have and still be awarded a C?
In #17-22, x has a normal distribution with the given mean( ) and standard deviation (σ). Find the
probailities.
17. P(x ≤ 34);
18. P(x ≥ 8.6);
= 46; σ = 2.4
= 10; σ = 1.3
19. P(72 ≤ x ≤ 113);
= 100; σ = 15
20. P(x ≤ 55);
= 51.6; σ = 3.2
21. P(x ≥ 61);
= 51.6; σ = 3.2
21. P(55 ≤ x ≤ 61);
= 51.6; σ = 3.2
22. A study found that the temperature of a ceramic furnace is normally distributed with a
mean temperature of 1425ºF and a standard deviation of 40º. What is the probability
that a randomly selected furnace will have a temperature less than 1505ºF?
23. On one measure of attractiveness, scores are normally distributed with a mean of 3.93
and a standard deviation of .84. Find the probability of randomly selecting a subject
with a measure of attractiveness that is greater than 2.07.
24. The mean number of absences per year for students at Sprayberry High School is 7, with a
standard deviation of 1.8. Natalie was absent 11 days last year. Explain how her absences
compare with the rest of the students. Use the probabilities to support your explanation.
25. The serum cholesterol levels in men aged 18 to 24 are normally distributed with a mean of 168
and a standard deviation of 32. If a man aged 18 to 24 is randomly selected, find the probability
that his serum cholesterol level is between 168 and 264.
26. In a survey of 504 people in the United States, about 11% said that the influx of new
technologies such as computers has left them feeling overwhelmed.
A) What is the margin of error for the survey? (Round to the nearest whole percent)
B) Give an interval that is likely to contain the exact percent of all people in the United States
who feel overwhelmed by the influx of new technologies.
27. In a survey of 250 Harrison students, 68% of them said that they have attended a high school
basketball game.
A)
What is the margin of error? (Round to the nearest whole percent)
B)
Give an interval that is likely to contain the exact percent who have attended a high
school basketball game.
28. A survey is conducted among elementary students to find out their favorite subject. Identify the
type of sample. Tell if it is biased and explain why or why not.
A)
Surveys are randomly distributed to 5th graders at lunch.
B)
Surveys are distributed to every other student entering the school.
C)
Surveys are left on the table in the front of the school.