Question 1

Which is true of the data shown in the histogram?  I. The distribution is approximately symmetric.
II) The mean and median are approximately equal.
III) The median and IQR summarize the data better than the mean and standard deviation.
A) III only
B) I only
C) I and III
D) I and II
E) I, II, and III

Accepted Answer

The answer of Which is true of the data shown...

Question 2

The Postmaster of a city's Post Office believes that a Normal model is useful in projecting
the number of letters which will be mailed during the day. They use a mean of 20,000
letters and a standard deviation of 250 letters. Draw and clearly label this model.

Accepted Answer

The answer of The Postmaster of a city's Post Office...

Question 3

A professor has kept records on grades that students have earned in his class. If he wants to
Examine the percentage of students earning the grades A, B, C, D, and F during the most recent
Term, which kind of plot could he make?
A) boxplot
B) histogram
C) timeplot
D) pie chart
E) dotplot

Accepted Answer

A pie chart is used to show the percentage distribution of different categories, such as grades in this case.

Question 4

City planners wanted to know how many people lived in a typical housing unit so they
compiled data from hundreds of forms that had been submitted in various city offices.
Summary statistics are shown
in the table. $\begin{array}{|c|c|}
\hline \bar{x} & 2.53 \text { people } \
\hline s & 1.40 \text { people } \
\hline \text { min } & 1 \
\hline \text { Q1 } & 1 \
\hline \text { median } & 2 \
\hline \text { Q3 } & 3 \
\hline \max & 10 \
\hline
\end{array}$

a. Notice that the minimum occupancy and the first quartile are the same. Explain how this can be.
b. The city classifies residences housing 4 or more people as "high occupancy". Would you consider 4 occupants to be unusually high? Explain.
c. The city bases their garbage disposal fee on the occupancy level of the home or apartment. The annual fee is $\$ 40$ plus $\$ 5$ per person, so a single occupant pays $\$ 45$ and the homes with 10 people pay $\$ 40 + \$ 5 ( 10 ) = \$ 90$ a year. What is the median fee paid? And the IQR?
d. What are the mean and standard deviation of the garbage disposal fees?

Accepted Answer

The answer of City planners wanted to know how many...

Question 5

A company's manufacturing process uses 500 gallons of water at a time. A "scrubbing"
machine then removes most of a chemical pollutant before pumping the water into a
nearby lake. Legally the treated water should contain no more than 80 parts per million of
the chemical, but the machine isn't perfect and it is costly to operate. Since there's a fine if
the discharged water exceeds the legal maximum, the company sets the machine to attain
an average of 75 ppm for the batches of water treated. They believe the machine's output
can be described by a Normal model with standard deviation 4.2 ppm. (SHOW
WORK)
a. What percent of the batches of water discharged exceed the 80ppm standard?
b. The company's lawyers insist that they not have more than 2% of the water over the
limit. To what mean value should the company set the scrubbing machine? Assume the
standard deviation does not change.
c. Because achieving a mean that low would raise the costs too much, they decide to leave
the mean set at 75 ppm and try to reduce the standard deviation to achieve the "only 2%
over" goal. Find the new standard deviation needed.
d. Explain what achieving a smaller standard deviation means in this context.

Accepted Answer

The answer of A company's manufacturing process uses 500 gallons...

Question 6

Adult female Dalmatians weigh an average of 50 pounds with a standard deviation of 3.3
pounds. Adult female Boxers weigh an average of 57.5 pounds with a standard deviation
of 1.7 pounds. One statistics teacher owns an underweight Dalmatian and an underweight
Boxer. The Dalmatian weighs 45 pounds, and the Boxer weighs 52 pounds. Which dog is
more underweight? Explain.

Accepted Answer

The answer of Adult female Dalmatians weigh an average of...

Question 7

During a budget meeting, local school board members decided to review class size
information to determine if budgets were correct. Summary statistics are shown in the
table. $$\begin{array} { | c | c | } 
\hline \bar { x } & 33.39 \text { students } \
\hline s & 5.66 \text { students } \
\hline \text { min } & 17 \
\hline \text { Q1 } & 29 \
\hline \text { median } & 33 \
\hline \text { Q3 } & 40 \
\hline \text { max } & 40 \
\hline
\end{array}$$ 
a. Notice that the third quartile and maximum class sizes are the same. Explain how this
can be.
b. The school district declares that classes with enrollments fewer than 20 students are "too
small". Would you consider a class of 20 students to be unusually small? Explain.
c. The school district sets the office supply budgets of their high schools on the enrollment
of students. The district budgets each class $12 plus $0.75 per student, so a class with one
student receives $12.75 and the classes with 40 students rec $$12 + 0.75 ( 40 ) = \$ 42$$ 
. What is
the median class budget for office supplies? And the IQR?
d. What are the mean and standard deviation of the class office supply budgets?

Accepted Answer

The answer of During a budget meeting, local school board...

Question 8

A statistics teacher gave her class a 15 point quiz. The summary statistics for the students'
scores are shown in the table. $$\begin{array} { | c | c | } 
\hline \bar { x } & 10.95 \text { points } \
\hline s & 2.481 \text { points } \
\hline \text { min } & 4 \
\hline \text { Q1 } & 9.5 \
\hline \text { median } & 12 \
\hline \text { Q3 } & 12 \
\hline \max & 15 \
\hline
\end{array}$$ 
a. Notice that the median score and the third quartile are the same. Explain how this can
be.
b. One student's parent heaped praise on him for scoring 13, saying it was an amazing
score. Comment on whether that praise is deserved using the summary statistics as
support.
c. To convert these raw scores to a score out of 100, the teacher multiplies each score by six,
then adds 10. (We can debate the wisdom of such a strategy later!). What is the median
converted score? And the IQR?
d. What are the mean and standard deviation of the converted test scores?

Accepted Answer

The answer of A statistics teacher gave her class a...

Question 9

At a large business, employees must report to work at 7:30 A.M. The arrival times of
employees can be described by a Normal model with mean of 7:22 A.M. and a standard
deviation of 4 minutes.
(SHOW WORK)
a. What percent of employees are late on a typical work day?
b. A psychological study determined that the typical worker needs five minutes to adjust to
their surroundings before beginning their duties. What percent of this business' employees
arrive early enough to make this adjustment?
c. Because late employees are a distraction and cost companies money, all employees need
to be on time to work. If the mean arrival time of employees does not change, what
standard deviation would the arrival times need to ensure virtually all employees are on
time to work?
d. Explain what achieving a smaller standard deviation means in the context of this
problem.

Accepted Answer

The answer of At a large business, employees must report...

Question 10

Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80,
And Section B had 20 students who had a mean score of 90. Overall, what was the approximate
Mean score for all of the students on the quiz?
A) 85.0
B) none of these
C) 84.3
D) 85.7
E) It cannot be determined.

Accepted Answer

The answer of Two sections of a class took the...

Question 11

Although most of us buy milk by the quart or gallon, farmers measure daily production in
pounds. Guernsey cows average 39 pounds of milk a day with a standard deviation of 8
pounds. For Jerseys the mean daily production is 43 pounds with a standard deviation of 5
pounds. When being shown at a state fair a champion Guernsey and a champion Jersey
each gave 54 pounds of milk. Which cow's milk production was more remarkable?
Explain.

Accepted Answer

The answer of Although most of us buy milk by...

Question 12

Light bulbs are measured in lumens (light output), watts (energy used), and hours (life). A
standard white light bulb has a mean life of 675 hours and a standard deviation of 50
hours. A soft white light bulb has a mean life of 700 hours and a standard deviation of 35
hours. At a local science competition, both light bulbs lasted 750 hours. Which light bulb's
life span was better? Explain.

Accepted Answer

The answer of Light bulbs are measured in lumens (light...

Question 13

School administrators collect data on students attending the school. Which of the following
Variables is quantitative?
A) grade point average
B) class (freshman, soph., junior, senior)
C) whether the student is in AP* classes
D) none of these
E) whether the student has taken the SAT

Accepted Answer

Grade point average is a quantitative variable because it is numerical and can be measured or counted.

Question 14

Owners of a minor league baseball team believe that a Normal model is useful in
projecting the number of fans who will attend home games. They use a mean of 8500 fans
and a standard deviation of 1500 fans. Draw and clearly label this model.

Accepted Answer

The answer of Owners of a minor league baseball team...

Question 15

Nickels minted in the United States are supposed to weigh 5.000 grams. Of course there is
some variation in that. The actual weights are pretty well represented by a normal model
with a mean of 5.000 g and a standard deviation of about 0.08 g. Draw and clearly label this
model.

Accepted Answer

The answer of Nickels minted in the United States are...

Question 16

Human body temperatures taken through the ear are typically 0.5° F higher than body
temperatures taken orally. Making this adjustment and using the 1992 Journal of the
American Medical Association article that reports average oral body temperature as 98.2° F, we will assume that a Normal model with an average of 98.7° F and a standard deviation
of 0.7° F is appropriate for body temperatures taken through the ear.
a. An ear temperature of 97° F may indicate hypothermia (low body temperature). What
percent of people have ear temperatures that may indicate hypothermia?
b. Find the interquartile range for ear temperatures.
c. A new thermometer for the ear reports that it is more accurate than the ear thermometers
currently on the market. If the average ear temperature reading remains the same and the
company reports an IQR of 0.5° F, find the standard deviation for this new ear
thermometer.

Accepted Answer

The answer of Human body temperatures taken through the ear...

Question 17

Dimes minted in the United States average 2.286 g with a standard deviation of 0.06 g.
Nickels have a mean of 5.000 g and a standard deviation of about 0.08 g. A couple
chemistry students were trying out their teacher's new scale by weighing a bunch of coins.
They found a nickel that weighed 5.19 g and a dime that weighed 2.45 g. Which coin was
more exceptionally heavy? Explain.

Accepted Answer

The answer of Dimes minted in the United States average...

Question 18

The lifespans of a particular brand of graphing calculator are approximately normally
distributed with a mean of 620 days from the purchase date and a standard deviation of 82
days. They will provide a warranty that guarantees a replacement if the calculator stops
working within the specified time frame, and are trying to decide what time frame to use.
a. If the company sets the warranty at a year and a half (say 540 days), what proportion of
calculators will they have to replace?
b. The company does not want to have to replace more than 1% of the calculators they sell.
What length of time should they set for the warranty?
c. The company would like to set the warranty for 540 days, and still replace no more than
1% of the calculators sold. Increasing the average life of the calculators is too expensive, but
they think they reduce the standard deviation of the lifespans. What standard deviation of
lifespans would be needed to make this happen?
d. Explain what achieving a smaller standard deviation means in this context.

Accepted Answer

The answer of The lifespans of a particular brand of...

Question 19

Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true?
I. You got 75% on the test.
II. You can't really tell what this means without knowing the standard deviation.
III. You can't really tell what this means unless the class distribution is nearly Normal.
A) III only
B) II and III
C) II only
D) I only
E) none of these

Accepted Answer

The 3rd quartile means you scored higher than 75% of the class, not that you got a 75% on the test. It doesn't require knowledge of standard deviation or a normal distribution to interpret quartiles.

Question 20

Which of the following variables would most likely follow a Normal model?
A) all of these
B) family income
C) scores on an easy test
D) weights of adult male elephants
E) heights of singers in a co-ed choir

Accepted Answer

The answer of Which of the following variables would most...

Quiz 8: Regression, Associations, and Predictive Modeling

Which is true of the data shown in the histogram? I. The distribution is approximately symmetric. II) The mean and median are approximately equal. III) The median and IQR summarize the data better than the mean and standard deviation.

The Postmaster of a city's Post Office believes that a Normal model is useful in projecting the number of letters which will be mailed during the day. They use a mean of 20,000 letters and a standard deviation of 250 letters. Draw and clearly label this model.

A professor has kept records on grades that students have earned in his class. If he wants to Examine the percentage of students earning the grades A, B, C, D, and F during the most recent Term, which kind of plot could he make?

Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80, And Section B had 20 students who had a mean score of 90. Overall, what was the approximate Mean score for all of the students on the quiz?

School administrators collect data on students attending the school. Which of the following Variables is quantitative?

Owners of a minor league baseball team believe that a Normal model is useful in projecting the number of fans who will attend home games. They use a mean of 8500 fans and a standard deviation of 1500 fans. Draw and clearly label this model.

Nickels minted in the United States are supposed to weigh 5.000 grams. Of course there is some variation in that. The actual weights are pretty well represented by a normal model with a mean of 5.000 g and a standard deviation of about 0.08 g. Draw and clearly label this model.

Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true? I. You got 75% on the test. II. You can't really tell what this means without knowing the standard deviation. III. You can't really tell what this means unless the class distribution is nearly Normal.

Which of the following variables would most likely follow a Normal model?