Question1The Tri-City School District has instituted a zero-tol.docx

Question1:
The Tri-City School District has instituted a zero-tolerance
policy for students carrying any objects that could be used as
weapons. The following data give the number of students
suspended during each of the past 12 weeks for violating this
school policy.
Find the mean, median, and mode.
Round your answers to two decimal places, where appropriate.
Mean = Median = Mode =
Question 2:
Recall the following from section 3.1 of the text. Mean : The
mean for ungrouped data is obtained by dividing the sum of all
values by the number of values in the data set. Median: The
median is the value of the middle term in a data set that has
been ranked in increasing order. If there is an even number of
data, find the average of the two middle data values. Mode:
The mode is the value that occurs with the highest frequency in
a data set. If there are more than one data values with the
highest frequency in a data set, we will have multiple modes. If
all data values have the same frequency of occurrences, then the
data set has no mode.
26,32,27,23,34,33,29,43,23,28
(a) Arrange the data in increasing order:
(b) Calculate the mean. The mean =
Question 3:
The following data represent the 2011 guaranteed salaries (in
thousands of dollars) of the head coaches of the final eight
teams in the 2011 NCAA Men's Basketball Championship. The
data represent the 2011 salaries of basketball coaches of the
following universities, entered in that order: Arizona, Butler,
Connecticut, Florida, Kansas, Kentucky, North Carolina, and
Virginia Commonwealth. (Source: www.usatoday.com)

1950,434,2300,3575,3376,3800,1655,418
Compute the range, variance and standard deviation for these
data.
Round your answers to the nearest integer, where appropriate.
Range = $
Variance =
Standard deviation = $
Question 4:
The 2011 gross sales of all firms in a large city have a mean of
$3.6 million and a standard deviation of $0.7 million. Using
Chebyshev′s theorem, find a lower bound on the percentage of
firms in this city that had 2011 gross sales between $0.8 and
$6.4 million.
Round the answer to the nearest percent.
The lower bound on the percentage is at least %
Questiono 5:
The 2011 gross sales of all firms in a large city have a mean of
$2.4 million and a standard deviation of $ 0.6 million. Using
Chebyshev's theorem, find at least what percentage of firms in
this city had 2011 gross sales of $1.0 to $3.8 million. Round
your answer to the nearest whole number.
%
Question 6:
The following data give the weights (in pounds) lost by 15
members of a health club at the end of two months after joining
the club.
5 10 8 7 24 12 5 13 11 10 21 9 8 11 18
(a) Calculate the approximate value of the 82nd percentile,
denoted P82.
P82 =
(b) Find the percentile rank of 11.
Give the answer rounded to the nearest percent.
The percentile rank of 11 =
Question 7:
In a group of households, the national news is watched on one
of the following networks – ABC, CBS, or NBC. On a certain

day, four households from this group randomly and
independently decide which of these channels to watch. Let x be
the number of households among these four that decide to watch
news on ABC. Is x a discrete or a continuous random variable?
Question 8:
Classify the following random variable as discrete or
continuous.
The number of cars crossing a bridge on a given day.
Question 9:
The following table gives the probability distribution of a
discrete random variable x.
X0123456
P(X)0.120.190.280.150.100.070.06
Find the probability that x assumes a value in the interval 2 to
5.
P=
Question 10:
According to a survey, 15% of adults are against using animals
for research. Assume that this result holds true for the current
population of all adults. Let x be the number of adults who are
against using animals for research in a random sample of two
adults. Obtain the probability distribution of x.
XP(X)
0
1
2
Enter the exact answers.
Question 11:
The H2 Hummer limousine has eight tires on it. A fleet of 1224
H2 limos was fit with a batch of tires that mistakenly passed
quality testing. The following table lists the frequency
distribution of the number of defective tires on the 1224 H2
limos.

Number of defective tires
0
1
2
3
4
5
6
7
8
Number of H2 limos
65
202
336
328
203
73
13
3
1
Construct a probability distribution table for the numbers of
defective tires on these limos.
Round your answers to three decimal places.
x
P(x)
0
1
2
3

4
5
6
7
8
Calculate the mean and standard deviation for the probability
distribution you developed for the number of defective tires on
all 1224 H2 Hummer limousines.
Round your answers to three decimal places.
There is an average of defective tires per limo, with a standard
deviation of
tires.
Question12:
Let x have a normal distribution with a mean of 41.0 and a
standard deviation of 3.87. The z value for x = 43.46, rounded
to two decimal places, is:
the tolerance is +/-2%
Question 13:
For the standard normal distribution, the area between z = -0.30
and z = 0.57, rounded to four decimal places, is:
Question 14:
Find the mean and the sampling/nonsampling error.

Consider the following population of 10 numbers.
202513199151171730
Round answers to two decimal places.
Find the population mean.
Question 15:
Consider the following population of 10 numbers.
24 29 17 23 13 19 15 11 21 34
(a) Find the population mean.
Enter the exact answer.
μ=
(b) Rich selected one sample of nine numbers from this
population. The sample included the
numbers 24, 29, 17, 13, 19, 15, 11, 21 and 34. Calculate the
sampling mean and sampling error for this sample.
Round your answers to two decimal places.
The sample mean is and sampling error is
for this sample.
(c) Refer to part (b). When Rich calculated the sample mean,
she mistakenly used the
numbers 24, 29, 17, 13, 19, 15, 21, 21 and 34 to calculate the
sample mean.
Find the sampling and nonsampling errors in this case.
The sampling error is and nonsampling error is

in this case.
(d) List all samples of nine numbers (without replacement) that
can be selected from this population. Calculate the sample mean
and sampling error for each of these samples.
Sample
x¯
x¯-μ
29, 17, 23, 13, 19, 15, 11, 21, 34
24, 17, 23, 13, 19, 15, 11, 21, 34
24, 29, 23, 13, 19, 15, 11, 21, 34
24, 29, 17, 13, 19, 15, 11, 21, 34
24, 29, 17, 23, 19, 15, 11, 21, 34
24, 29, 17, 23, 13, 15, 11, 21, 34
24, 29, 17, 23, 13, 19, 11, 21, 34
24, 29, 17, 23, 13, 19, 15, 21, 34

24, 29, 17, 23, 13, 19, 15, 11, 34
24, 29, 17, 23, 13, 19, 15, 11, 21
STAT 200 Final ExaminationSpring 2017OL4/US2Page 1 of 10
STAT200Introduction to
StatisticsName______________________________
Final Examination: Spring 2017OL4/US2Instructor
__________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and
other course materials as you work on the exam, and you may
use a calculator.
Record your answers and work in this document.
Answer all 20 questions. Make sure your answers are as
complete as possible. Show all of your work and reasoning. In
particular, when there are calculations involved, you must show
how you come up with your answers with critical work and/or
necessary tables. Answers that come straight from calculators,
programs or software packages without explanation will not be
accepted.If you need to use technology to aid in your
calculation, you haveto cite the source and explain how you get
the results. For example, state the Excel function along with the
required parameters when using Excel; describe the detailed
steps when using a hand-held calculator; or provide the URL
and detailed steps when using an online calculator, and so on.

Show all supporting work and write all answers in the spaces
allotted on the following pages. You may type your work using
plain-text formatting or an equation editor, or you may hand-
write your work and scan it. In either case, show work neatly
and correctly, following standard mathematical conventions.
Each step should follow clearly and completely from the
previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither
collaboration nor consultation with others is allowed.It is a
violation of the UMUC Academic Dishonesty and Plagiarism
policy to use unauthorized materials or work from others.Your
exam will receive a zero grade unless you complete the
following honor statement.
(
Please sign (or type) your name below the following honor
statement:
I understand that i
t is a violation of the UMUC Academic Dishonesty and
Plagiarism policy to use unauthorized materials or work from
others.
I promise that I did not discuss any aspect of this exam with
anyone other than my instructor.
I further promise that I neither gave nor received any
unauthorized assistanceon this exam, and that the work
presented herein is entirely my own.
Name ____________
______
___
Date___________________
)
Record your answers and work.
Problem Number

Solution
1
Answer:
(a)
(b)
(c)
(d)
(e)
Justification:

2
Answer:
(a)
(b)
(c)
Justification:
3

Answer:
(a)
IQ Scores
Frequency
Cumulative Relative Frequency
50 - 69
23
70 - 89
249
90 -109
0.743
110 - 129
130 - 149
25
Total
1000

(b)
(c)
Work for (a) and (b):
4
Answer:
(a)
(b)
(c)
Justification:

5
Answer:
(a)
(b)
6
Answer:
(a)

(b)
Work for (b):
7
Answer:
(a)
(b)

8
Answer:
(a)
(b)
9
Answer:
(a)

x
P(x)
0
1
2
Total
(b)

10
Answer:
(a)
(b)
Work for (b) :

11
Answer:
(a)
(b)
12
Answer:
(a)
(b)

13
Answer:
Work:
14
Answer:
Work:

15
Answer:
(a)
(b)
(c)
(d)
Work for (b) and (c):

16
Answer:
(a)
(b)
(c)
(d)

17
Answers:
(a)
(b)
(c)
(d).

18
Answer:
(a)
(b)
(c)
(d)

19
Answer:
(a)
(b)

20
Answer:
(a)
Source of Variation
Sum of Squares
(SS)
Degrees of Freedom (df)
Mean Square
(MS)
Factor
(Between)
27.82
Error
(Within)
Total
543.05
159

N/A
(b)
(c)
(d)
Work for (a), (b) and (c):

STAT 200: Introduction to Statistics Final Examination,
Spring 2017 OL4/US2 Page 1 of 8
STAT 200
OL4 / US2 Sections
Final Exam
Spring 2017
The final exam will be posted at 12:01 am on May 5, and it is
due

at 11:59 pm on May 7, 2017. Eastern Time is our reference
time.
This is an open-book exam. You may refer to your text and
other course materials
as you work on the exam, and you may use a calculator. You
must complete the
exam individually. Neither collaboration nor consultation with
others is allowed.
It is a violation of the UMUC Academic Dishonesty and
Plagiarism policy to use
unauthorized materials or work from others.
Answer all 20 questions. Make sure your answers are as
complete as possible.
Show all of your supporting work and reasoning. Answers that

come straight
from calculators, programs or software packages without any
explanation will not
be accepted. If you need to use technology (for example, Excel,
online or hand-
held calculators, statistical packages) to aid in your calculation,
you must cite the
sources and explain how you get the results.
Record your answers and work on the separate answer sheet
provided.
This exam has 20 questions; 5% for each question.
You must include the Honor Pledge on the title page of your
submitted final exam.
Exams submitted without the Honor Pledge will not be

accepted.
1. True or False. Justify for full credit.
(a) If A and B are any two events, then P(A AND B) ≤ P(A OR
B).
(b) If the variance of a data set is 0, then all the observations in
this data set must be zero.
(c) The volume of milk in a jug of milk is 128 oz. The value
128 is from a discrete data set.
(d) When plotted on the same graph, a distribution with a mean
of 60 and a standard deviation

of 5 will look less spread out than a distribution with a mean of
40 and standard deviation
of 8.
(e) In a left-tailed test, the value of the test statistic is -2. The
test statistic follows a
distribution with the distribution curve shown below. If we
know the shaded area is 0.97,
then we do not have sufficient evidence to reject the null
hypothesis at 0.05 level of
significance.
2. Choose the best answer. Justify for full credit.
(a) A study was conducted at a local college to analyze the
average GPA of students graduated

from UMUC in 2016. 100 students graduated from UMUC in
2016 were randomly
selected, and the average GPA for the group is 3.5. The value
3.5 is a
(i) statistic
(ii) parameter
(iii) cannot be determined
(b) The hotel ratings are usually on a scale from 0 star to 5
stars. The level of this
measurement is
(i) interval
(ii) nominal

(iii) ordinal
(iv) ratio
(c) The quality control department of a semiconductor
manufacturing company tests every 100th
product from the assembly line. This type of sampling is called:
(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified

3. The frequency distribution below shows the distribution for
IQ scores for a random sample of
1000 adults. (Show all work. Just the answer, without
supporting work, will receive no credit.)
IQ Scores Frequency
Cumulative Relative
Frequency
50 - 69 23
70 - 89 249
90 -109
0.743
110 - 129

130 - 149 25
Total 1000
(a) Complete the frequency table with frequency and cumulative
relative frequency. Express the
cumulative relative frequency to three decimal places.
(b) What percentage of the adults in this sample has an IQ score
between 90 and 129, inclusive?
(c) Which of the following IQ score groups does the
median of this distribution belong to?
70 – 89, 90 – 109, or 110 – 129? Why?
4. The five-number summary below shows the grade distribution
of a STAT 200 quiz for a
sample of 160 students.

Answer each question based on the given information, and
explain your answer in each case.
(a) What is the interquartile range in the grade distribution?
(b) Which of the following score bands has the fewest students?
(i) 30 - 50
(ii) 50 - 70

(iii) 70 - 90
(Iv) Cannot be determined
(c) How many students in the sample are in the score band
between 50 and 70?
5. Consider selecting one card at a time from a 52-card deck.
What is the probability that the first
card is an ace and the second card is also an ace? (Note: There
are 4 aces in a deck of cards)
(Show all work. Just the answer, without supporting work, will
receive no credit.)
(a) Assuming the card selection is with replacement.
(b) Assuming the card selection is without replacement.

6. There are 1000 juniors in a college. Among the 1000 juniors,
300 students are taking
STAT200, and 150 students are taking PSYC300. There are 50
students taking both courses.
Let S be the event that a randomly selected student takes
STAT200, and P be the event that a
randomly selected student takes PSYC300. (Show all work. Just
the answer, without
supporting work, will receive no credit.)
(a) Provide a written description of the complement event of (S
OR P).
(b) What is the probability of complement event of (S OR P)?
7. Consider rolling a fair 6-faced die twice. Let A be the event
that the sum of the two rolls is at

most 6, and B be the event that the first one is a multiple of 3.
(a) What is the probability that the sum of the two rolls is at
most 6 given that the first one is a
multiple of 3? Show all work. Just the answer, without
supporting work, will receive no credit.
(b) Are event A and event B independent? Explain.
8. Answer the following two questions. (Show all work. Just
the answer, without supporting
work, will receive no credit).
(a) Mimi has seven books from the Statistics is Fun series. She
plans on bringing three of the
seven books with her in a road trip. How many different ways
can the three books be selected?

(b) UMUC Stat Club must appoint a president, a vice president,
and a treasurer. There are 8
qualified candidates. How many different ways can the officers
be appointed?
9. Let random variable x represent the number of heads when a
fair coin is tossed two times.
(a) Construct a table describing the probability distribution.
(b) Determine the mean and standard deviation of x. (Round the
answer to two decimal places)

10. Mimi plans on growing tomatoes in her garden. She has 20
cherry tomato seeds. Based on her
experience, the probability of a seed turning into a seedling is
0.60.
(a) Let X be the number of seedlings that Mimi gets. As we
know, the distribution of X is a binomial
probability distribution. What is the number of trials (n),
probability of successes (p) and probability of
failures (q), respectively?
(b) Find the probability that she gets at least 15 cherry tomato
seedlings. (round the answer to 3 decimal
places) Show all work. Just the answer, without supporting
work, will receive no credit.
11. The heights of pecan trees are normally distributed with a

mean of 10 feet and a standard
deviation of 2 feet. Show all work. Just the answer, without
supporting work, will receive no
credit.
(a) What is the probability that a randomly selected pecan tree
is between 9 and 12 feet tall? (round the
answer to 4 decimal places)
(b) Find the 80th percentile of the pecan tree height
distribution. (round the answer to 2 decimal places)
12. Based on the performance of all individuals who tested
between July 1, 2012 and June 30, 2015,
the GRE Quantitative Reasoning scores are normally distributed
with a mean of 152.47 and a

standard deviation of 8.93.
(https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). Show all
work. Just the answer, without supporting work, will receive no
credit.
(a) Consider all random samples of 36 test scores. What is the
standard deviation of the sample
means? (Round your answer to three decimal places)
(b) What is the probability that 36 randomly selected test scores
will have a mean test score that is
between 148 and 152?
13. A survey showed that 1200 of the 1600 adult respondents
believe in global warming. Construct
a 95% confidence interval estimate of the proportion of adults
believing in global warming.
Show all work. Just the answer, without supporting work, will
receive no credit.

14. A city built a new parking garage in a business district. For
a random sample of 100 days, daily
fees collected averaged $2,000, with a standard deviation of
$500. Construct a 90% confidence
interval estimate of the mean daily income this parking garage
generates. Show all work. Just
the answer, without supporting work, will receive no credit.
15. A researcher claims the proportion of auto accidents that
involve teenage drivers is less than
20%. ABC Insurance Company checks police records on 200

randomly selected auto
accidents and notes that teenagers were at the wheel in 32 of
them.
Assume the company wants to use a 0.05 significance level to
test the researcher’s claim.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the
correct test statistic, without supporting
(c) Determine the P-value for this test. Show all work; writing
the correct P-value, without
(d) Is there sufficient evidence to support the researcher’s claim
that the proportion of auto accidents that

involve teenage drivers is less than 20%? Explain.
16. Mimi was curious if regular excise really helps weight loss,
hence she decided to perform a
hypothesis test. A random sample of 5 UMUC students was
chosen. The students took a 30-
minute exercise every day for 6 months. The weight was
recorded for each individual before
and after the exercise regimen. Does the data below suggest
that the regular exercise helps
weight loss? Assume Mimi wants to use a 0.05 significance
level to test the claim.
Weight (pounds)
Subject Before After
1 190 180

2 170 160
3 185 175
4 160 160
5 200 190
(c) Determine the p-value. Show all work; writing the correct
critical value, without supporting
(d) Is there sufficient evidence to support the claim that regular
exercise helps weight loss? Justify

your conclusion.
17. In a pulse rate research, a simple random sample of 400 men
results in a mean of 80 beats per
minute, and a standard deviation of 10.8 beats per minute.
Based on the sample results, the
researcher concludes that the pulse rates of men have a standard
deviation greater than 10 beats
per minutes. Use a 0.05 significance level to test the
researcher’s claim.
(a) Identify the null hypothesis and alternative hypothesis.

correct test statistic, without
(c) Determine the P-value for this test. Show all work; writing
the correct P-value, without
(d) Is there sufficient evidence to support the researcher’s
claim? Explain.
18. The UMUC Daily News reported that the color distribution
for plain M&M’s was: 40%
brown, 20% yellow, 20% orange, 10% green, and 10% tan.
Each piece of candy in a random
sample of 100 plain M&M’s was classified according to color,
and the results are listed below.
Use a 0.05 significance level to test the claim that the published
color distribution is correct.

Show all work and justify your answer.
Color Brown Yellow Orange Green Tan
Number 42 18 15 7 18
(c) Determine the P-value. Show all work; writing the correct P-
value, without supporting work,
will receive no credit.
(d) Is there sufficient evidence to support the claim that the
published color distribution is correct?

Justify your answer.
19. A STAT 200 instructor believes that the average quiz score
is a good predictor of final exam
score. A random sample of 10 students produced the following
data where x is the average quiz
score and y is the final exam score.
x 80 93 50 60 100 40 85 70 75 85
y 70 96 50 63 96 38 83 60 77 87
(a) Find an equation of the least squares regression line. Show
all work; writing the correct
equation, without supporting work, will receive no credit.
(b) Based on the equation from part (a), what is the predicted
final exam score if the average quiz

score is 95? Show all work and justify your answer.
20. A study of 8 different weight loss programs involved 160
subjects. Each of the 8 programs had
20 subjects in it. The subjects were followed for 12 months.
Weight change for each subject was
recorded. We want to test the claim that the mean weight loss is
the same for the 8 programs.
(a) Complete the following ANOVA table with sum of squares,
degrees of freedom, and mean

square (Show all work):
Source of Variation
Sum of Squares
(SS)
Degrees of Freedom
(df)
Mean Square
(MS)
Factor
(Between)
27.82
Error
(Within)

Total 543.05 159
N/A
(c) Determine the P-value. Show all work; writing the correct P-
value, without supporting work,
will receive no credit.
(d) Is there sufficient evidence to support the claim that the
mean weight loss is the same for the 8
programs at the significance level of 0.05? Explain.

Question1The Tri-City School District has instituted a zero-tol.docx

Question1The Tri-City School District has instituted a zero-tol.docx

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