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Tallahassee Statewide
1/14/2017
Statistics Individual Test
All answers are exact unless specified in the question. E) NOTA is “None
of these answers”. Have fun!
1. Mr. Hale wants to sample the students at Jones High about the best location
to have pep rallies. Mr. Hale separates the students by grade level and then
samples 100 students randomly from each grade level. What type of sample did
Mr. Hale perform?
A) simple random sample B) multi-stage sample C) systematic sample
D) stratified sample
E) NOTA
2. There is a negative relationship between the number of semesters needed to
graduate college and the starting salary of their first job. Assume that the starting
salary of their first job is the response variable and the number of semesters
needed to graduate college is the explanatory variable. The average number of
semesters needed to graduate college is 8 with a standard deviation of 2. The
average starting salary of their first job is $43,000 with a standard deviation of
$5,000. The coefficient of determination between the variables is .3844. Find
the equation of the line of best fit between the variables in slope intercept form.
A) y = -0.00248x + 43000
C) y = -1550x + 55400
B) y = 0.000248x + 43000
D) y = 1550x + 30600
E) NOTA
3. Given the following: P(A) =.59, P(B) =.54, P(A'Ç B') =.28 , find P(A Ç B) .
A) 0.72
B) 0.41
C) 0.18
D) 0.13
E) NOTA
4. Given the following statistical measures: (mean, median, range, interquartile
range, standard deviation, correlation coefficient), how many of them can never
be negative?
A) 1
B) 2
C) 3
D) 4
E) NOTA
5. Given the following: x = 63, sx = 6, y = 84, sy = 4, r =.72 , find the value of the
standard deviation for the set (x + y).
A) 10
B)
2 541
5
C) 2 13
D)
2 109
5
E) NOTA
6. Mr. Sherry gives a History test. The results of the test form a normal
distribution. Carlos scores an 87 on the test. 6.3% of the class scores higher
than Carlos. Rachel scores a 62 on the test. 12.3% of the class scores lower
than Rachel. Round each z-score to two decimal places. Find the mean of the
History test, rounded to one decimal place.
A) 76.2
B) 74.5
C) 73.6
D) 72.8
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E) NOTA
Tallahassee Statewide
1/14/2017
Statistics Individual Test
7. Given the following set of data: (34, 99, 20, 80, 95, 22, 37, 1, 93, 11), find the
range of values used to determine if the data set has any outliers. The answers
are in the form (minimum, maximum).
A) (-89.5, 202.5)
B) (-72, 172)
C) (-53, 146)
D) (1, 99)
E) NOTA
8. Each year, Mrs. Minns has a spinning wheel fundraiser at the school carnival.
It costs $5 to spin the wheel. There are 20 equal size sections on the wheel.
The breakdown of the sections are as follows: ten $1 sections, five $2 sections,
three $5 sections, one $10 section and one $20 section. Find the expected profit
Mrs. Minns makes from a spin of the wheel.
A) $3.25
B) $2.60
C) $2.40
D) $1.75
E) NOTA
9. Mr. Kenyon gives daily quizzes to his classes. Today’s quiz is multiple
choice. It is a three question quiz in which question one has four choices,
question two has three choices and question three has two choices. Jessica
hasn’t studied for the quiz and will randomly guess on each question. Find the
probability that Jessica gets one question correct on the quiz.
A)
11
24
B)
4
9
C)
13
36
D)
1
3
E) NOTA
10. Find the standard deviation of the following discrete distribution:
X
1
13
28
45
68
85
97
P(X)
.04
.11
.16
.24
.14
.17
.13
Round your answer to two decimal places.
A) 36.54
B) 33.83
C) 31.76
D) 29.41
E) NOTA
11. A marketing consultant is studying the use of the weekly sales ad to increase
sales at the local grocery store. What is the minimum number of customers that
the consultant should study if they want to be accurate within $5 of the true
amount of sales at the 95% confidence level? Round the test statistic needed to
two decimal places. Assume that s = $12 .
A) 6
B) 15
C) 16
D) 23
E) NOTA
12. Find the standard deviation of the following data set:
4, 8, 9, 10, 12, 13, 15, 17, 19, 23
A) 4 2
B)
12 5
5
C) 5.37
D) 5.66
2
E) NOTA
Tallahassee Statewide
1/14/2017
Statistics Individual Test
13. The average rainfall in Tallahassee is 62 inches per year. What is the
standard deviation if 16.6% of the years have rainfall above 74 inches? Assume
that yearly rainfall is normally distributed and that the test statistic needed is to
two decimal places. Round your final answer to two decimal places.
A) 8.66
B) 10.52
C) 12.37
D) 14.39
E) NOTA
14. Sean Maguire completed 59% of his passes last season for Florida State. In
his first game of the year, Sean attempted 28 passes. Assume each pass is
independent. Find the probability that Sean completed more than 16 and less
than 22 passes in the game. Round your answer to four decimal places.
A) 0.4993
B) 0.4830
C) 0.3490
D) 0.3327
E) NOTA
15. The following are parts of the probability distributions for the random
variables x and y.
x
1
2
3
4
y
1
2
3
P(x)
?
.31
.18
?
P(y)
.22
?
?
If x and y are independent and the joint probability P(x = 2, y = 2) = .1581 and
P(x = 4, y = 3) = .0675, what is P(x = 1, y = 2)?
A) 0.1326
B) 0.1275
C) 0.0995
D) 0.0682
E) NOTA
16. Suppose x and y are random independent variables with
x = 72, sx = 6, y = 91, sy =10 . What is the standard deviation of the random
variable (5x – 3y)?
A) 0
B) 60
C) 30 2
D) 4 30
E) NOTA
17. There are 130 students surveyed. 45 take Biology, 47 take Chemistry and
51 take Physics. 20 take Biology only, 27 take Chemistry only and 32 take
Physics only. 6 students take all three classes. Find the number of students
who don’t take any of the three courses.
A) 19
B) 22
C) 23
D) 30
E) NOTA
18. Which of the following is a resistant measure?
A) mean
B) standard deviation
D) correlation coefficient
E) NOTA
C) range
19. Stacy is trying to get her dog Dakota to fetch and return a ball to her. Dakota
is successful 36% of the time fetch and returning the ball. Stacy takes Dakota to
the dog park and will not leave until Dakota fetches and returns a ball to her.
Find the probability that Dakota fetches and returns a ball by the third attempt.
A) 0.737856
B) 0.5904
C) 0.2304
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D) 0.147456
E) NOTA
Tallahassee Statewide
1/14/2017
Statistics Individual Test
20. A binomial distribution has a mean of 139.5 and a standard deviation of
3 589
. Find the number of trials in the distribution.
10
A) 155
B) 186
C) 225
D) 279
E) NOTA
21. Mrs. Ewart gives a Chemistry test. The results of the test are a mean of 58
and a standard deviation of 12. Mrs. Ewart curves the scores to create a mean
of 75 and a standard deviation of 6. Jake scores a 66 on the test. Find the value
of Jake’s curved score.
A) 74
B) 79
C) 81
D) 83
E) NOTA
22. Given two independent events A and B, P(A) = .68, P(B) = .47, find the
probability of the following:
P(A’|B) + P(B’|A)
A) 0.5108
B) 0.8304
C) 0.8496
D) 0.85
E) NOTA
23. Given a normal distribution, find the probability of randomly selecting a value
one standard deviation below the mean or three standard deviations above the
mean. Assume that the empirical percentages are used.
A) 0.1615
B) 0.323
C) 0.68
D) 0.837
E) NOTA
24. A veterinarian conducts an experiment to see the effects of food and
vitamins on hamsters’ health. Two new types of hamster food are going to be
compared with the standard hamster food. Each type of hamster food will be
given a vitamin C supplement or a placebo randomly. Each treatment will be
randomly given to 25 hamsters. Each hamster will be given an exam prior to the
experiment and then again after four weeks to determine the effect of the
treatment on the hamster. Find the total number of treatments used in the
experiment.
A) 2
B) 3
C) 4
D) 6
E) NOTA
25. There is a linear relationship between the midterm exam and the final exam
3
for Ms. Corbin’s History class. The equation is y = x + 52 , where x is the
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midterm exam and y is the final exam. Tasnia scores an 80 on the midterm
exam and an 73 on the final exam. Find the value of Tasnia’s residual.
A) -
5
3
B)
5
3
C) - 9
D) 9
E) NOTA
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Tallahassee Statewide
1/14/2017
Statistics Individual Test
26. 44% of the students at Smith High are boys. 8% of the boys and 15% of the
girls at Smith High drive to school. A student from Smith High is randomly
selected. Find the probability that the student is a girl, given that the student
does not drive to school.
A)
1101
1250
B)
595
1101
C)
119
250
D)
35
367
E) NOTA
27. In a frequency distribution of 5000 scores, the mean is to the right of the
median. The shape of the distribution is
A) symmetric
D) skewed to the left
B) bimodal
E) NOTA
C) skewed to the right
28. The SAT is a test used as a criteria to enter college. The current SAT test is
a maximum of 1600 points. Last year’s students who took the SAT had a normal
distribution with a mean score of 1030 and a standard deviation of 125. A
student is randomly selected. Find the probability that a student scored greater
than 1100, given that the student scored less than 1300. Round the final answer
to four decimal places.
A) 0.2922
B) 0.2877
C) 0.2766
D) 0.2724
E) NOTA
29. Natasha likes to eat M+M’s from Mr. Frost’s candy jar on his desk. Mr. Frost
see Natasha coming for her M+M. In the jar, there are 20 brown, 15 red and 10
green M+M’s. Mr. Frost tells Natasha to choose an M+M, one at a time and with
replacement. Once Natasha chooses a red M+M, she may consume it and go
back to her desk. Find the standard deviation of Natasha’s M+M selection.
A)
6
B)
3 5
4
C)
3 7
2
D)
30
3
E) NOTA
30. There is a data set X. The values in data set X are positive integers less
than 200 with an odd number of integral factors. Find the mean of the data set X.
A) 64
B) 72.5
C) 75
D) 100.5
E) NOTA
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