Question 1

Concrete thickness A roadway construction process uses a machine that pours concrete
onto the roadway and measures the thickness of the concrete so the roadway will measure
up to the required depth in inches. The concrete thickness needs to be consistent across the
road, but the machine isn't perfect and it is costly to operate. Since there's a safety hazard if
the roadway is thinner than the minimum 23 inch thickness, the company sets the machine
to average 26 inches for the batches of concrete. They believe the thickness level of the
machine's concrete output can be described by a Normal model with standard deviation
1.75 inches. [Show work]
a. What percent of the concrete roadway is under the minimum depth?
b. The company's lawyers insist that no more than 3% of the output be under the limit.
Because of the expense of operating the machine, they cannot afford to reset the mean to a
higher value. Instead they will try to reduce the standard deviation to achieve the "only 3%
under" goal. What standard deviation must they attain?
c. Explain what achieving a smaller standard deviation means in this context.

Accepted Answer

The answer of Concrete thickness A roadway construction process uses...

Question 2

Cellphones ConsumerReports.org evaluated the price and performance of 99 models of
cellphones. Computer output gives these summaries for the prices: $$\begin{array} { | c | c | c | c | c | c | c | c | c | } 
\hline \text { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } & \text { MidRange } & \text { Mean } & \text { TrMean } & \text { SD } \
\hline 0 & 0 & 50 & 200 & 400 & 200 & 96.36 & 90.21 & 107.23 \
\hline
\end{array}$$ 
a. Were any of the prices outliers? Explain how you made your decision.
b. One of the manufacturers advertises a cellphone "economy-priced at only $31.95".
Would you consider that to be a very low price? Explain.

Accepted Answer

The answer of Cellphones ConsumerReports.org evaluated the price and performance...

Question 3

The standard deviation of the data displayed in this dotplot is most likely to be …

Accepted Answer

The answer of The standard deviation of the data displayed...

Question 4

Suppose that a Normal model describes the acidity (pH) of rainwater, and that water tested after
Last week's storm had a z-score of 1.8. This means that the acidity of that rain …

Accepted Answer

A z-score of 1.8 indicates that the pH of the rainwater was 1.8 standard deviations higher than the average pH of rainwater.

Question 5

The ages of people attending the opening show of a new movie are summarized in the ogive
Shown. Estimate the IQR of the ages.

Accepted Answer

The answer of The ages of people attending the opening...

Question 6

Book sales A publishing company pays its sales staff $600 a week plus a commission of
$0.50 per book sold. For example, a salesman who sold 440 books earned 600 + 0.50(440) =
$820.
a. The table shows summary statistics for the number of books the large sales staff sold last
week. Fill in the table to show the statistics for the pay these people earned. $$\begin{array} { | l | c | l | } 
\hline \text { Statistic } & \text { Books Sold } & \text { \$ Earned } \
\hline \text { Mean } & 640 & \
\hline \text { St. dev. } & 360 & \
\hline \text { IQR } & 450 & \
\hline \text { Maximum } & 1420 & \
\hline
\end{array}$$ 
b. The newest employee had a pretty good week. Among all the salespeople her pay
corresponded to a z-score of +1.80. What was the z-score of the number of books she sold?

Accepted Answer

The answer of Book sales A publishing company pays its...

Question 7

Repair bills An automobile service shop reported the summary statistics shown for repair
bills (in $) for their customers last month. $$\begin{array} { | l | r | } 
\hline \text { Min } & 27 \
\text { Q1 } & 88 \
\text { Median } & 132 \
\text { Q3 } & 308 \
\text { Max } & 1442 \
\text { Mean } & 284 \
\text { SD } & 140 \
\hline
\end{array}$$ 
a. Were any of the bills outliers? Show how you made your decision.
b. After checking out a problem with your car the service manager gives you an estimate of
"only $90." Is he right to imply that your bill will be unusually low? Explain briefly.

Accepted Answer

The answer of Repair bills An automobile service shop reported...

Question 8

Salary conversions You learn that your company is sending you and several other
employees to staff a new office in China. While there everyone will earn the equivalent of
their current salary, converted to Chinese currency at the rate of 8 yuans per dollar. In
addition, everyone will earn a weekly foreign living allowance of 200 yuans. For example,
since you are earning $1000 per week, your weekly salary in China will be 1000 x 8 + 200 =
8200 yuans.
a. Shown are some summary statistics describing the current salaries of this group being
sent overseas. Fill in the table to show what these statistics will be for the salaries you all
will earn while in China. $$\begin{array} { | l | c | l | } 
\hline \text { Statistic } & \text { In the US } & \text { In China } \
\hline \text { Minimum salary } & \$ 400 & \
\hline \text { Standard deviation } & \$ 250 & \
\hline \text { Median } & \$ 750 & \
\hline \text { IQR } & \$ 300 & \
\hline
\end{array}$$ 
b. Among this group of employees going to China, your US salary has a $$z - s c o r e \text { of } + 1.20$$ 
What will your new z-score be, based on everyone's China salary?

Accepted Answer

The answer of Salary conversions You learn that your company...

Question 9

We might choose to display data with a stemplot rather than a boxplot because a stemplot
I. reveals the shape of the distribution.
II. is better for large data sets.
III. displays the actual data.

Accepted Answer

A stemplot reveals the shape of the distribution and displays the actual data, making options I and III correct. However, stemplots are not ideal for large data sets, so option II is incorrect.

Question 10

The mean number of hours worked for the 30 males was 6, and for the 20 females was 9. The
Overall mean number of hours worked …

Accepted Answer

The overall mean is calculated by taking the total hours worked by both groups and dividing by the total number of individuals: (30*6 + 20*9) / (30+20) = 7.2.

Question 11

Paying for purchases One day a store tracked the way shoppers paid for their purchases.
Their data are summarized in the table.  
a. What percent of men paid cash?
b. What is the conditional relative frequency distribution of payment method for women?
c. If you wanted to show the association between gender and method of payment visually,
what kind of graph would you make? (Just name it.)
d. Is there evidence of an association between gender and method of payment? Explain
briefly.

Accepted Answer

The answer of Paying for purchases One day a store...

Question 12

The United States Census collects data on many variables about individuals and households.
Which variable is categorical?

Accepted Answer

Type of residence is a categorical variable because it describes a characteristic or quality that can be divided into different categories or groups, such as apartment, house, or condo.

Question 13

We collect these data from 50 male students. Which variable is categorical?

Accepted Answer

Eye color is a categorical variable because it describes a characteristic that can be divided into distinct categories or groups, such as blue, brown, or green.

Question 14

Which of these variables is most likely to be bimodal?

Accepted Answer

The number of cigarettes smoked daily is most likely to be bimodal because there are two distinct groups of people: smokers and non-smokers.

Question 15

Environmental researchers have collected rain acidity data for several decades. They want to see if
There is any evidence that attempts to reduce industrial pollution have produced a trend toward
Less acidic rainfall. They should display their data in a(n)…

Accepted Answer

A timeplot is appropriate for displaying data collected over time to identify trends or patterns, such as changes in rain acidity.

Question 16

Which type of plot would be most appropriate to display the responses to type of residence?

Accepted Answer

A pie chart is most appropriate for displaying categorical data, such as types of residence, as it shows the proportion of each category within the whole.

Question 17

Which of these variables is most likely to follow a Normal model?

Accepted Answer

Head circumference is a continuous variable that is likely to be normally distributed in a population, as many biological measurements tend to follow a normal distribution.

Question 18

Copy machines A manufacturer claims that lifespans for their copy machines (in months)
can be described by a Normal model N(42,7). Show your work.
a. Draw and clearly label the model.  
b. A company with a several large office buildings buys 200 of these copiers. The salesman
tells the boss "190 (95%) of your new copiers will last between _____ and _____ months."
Comment on this claim.
c. What is the 3rd quartile of copier lifespans?
d. What percent of the copiers are expected to fail before 36 months?
e. The manufacturer wants to reduce the 36-month failure rate to only 10%. Assuming the
mean lifespan will stay the same, what standard deviation must they achieve?
f. Briefly explain what that change in standard deviation means in this context.
g. A competing manufacturer says that not only will 90% of their copiers last at least 36
months, 65% will last at least 42 months. What Normal model parameters is that
manufacturer claiming? Show your work.

Accepted Answer

The answer of Copy machines A manufacturer claims that lifespans...

Question 19

Exercising Owners of an exercise gym believe that a Normal model is useful in projecting
the number of clients who will exercise in their gym each week. They use a mean of 800
clients and a standard deviation of 90 clients.
a. Draw and clearly label this model.  
b. What is the first quartile of the weekly number of clients? [Show work]
c. An owner of another gym reports that 5% of the time their gym has fewer than 450
clients, and 40% of the time the gym has more than 1085 clients. What parameters should
that owner use for his Normal model?

Accepted Answer

The answer of Exercising Owners of an exercise gym believe...

Question 20

Which is true of the data whose distribution is shown?  I. The distribution is skewed to the right.
II) The mean is probably smaller than the median.
III) We should summarize with mean and standard deviation.

Accepted Answer

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

Quiz 8: Regression, Associations, and Predictive Modeling

The standard deviation of the data displayed in this dotplot is most likely to be …

Suppose that a Normal model describes the acidity (pH) of rainwater, and that water tested after Last week's storm had a z-score of 1.8. This means that the acidity of that rain …

The ages of people attending the opening show of a new movie are summarized in the ogive Shown. Estimate the IQR of the ages.

We might choose to display data with a stemplot rather than a boxplot because a stemplot I. reveals the shape of the distribution. II. is better for large data sets. III. displays the actual data.

The mean number of hours worked for the 30 males was 6, and for the 20 females was 9. The Overall mean number of hours worked …

The United States Census collects data on many variables about individuals and households. Which variable is categorical?

We collect these data from 50 male students. Which variable is categorical?

Which of these variables is most likely to be bimodal?

Environmental researchers have collected rain acidity data for several decades. They want to see if There is any evidence that attempts to reduce industrial pollution have produced a trend toward Less acidic rainfall. They should display their data in a(n) …

Which type of plot would be most appropriate to display the responses to type of residence?

Which of these variables is most likely to follow a Normal model?

Which is true of the data whose distribution is shown? I. The distribution is skewed to the right. II) The mean is probably smaller than the median. III) We should summarize with mean and standard deviation.