7-32. SeaFair Fashions relies on its sales force of 220 to do an initial screening of all new fashion. The company is currently bringing out a new line of swimwear and has invited 40 salespeople to its Orlando home office. An issue of constant concern to the SeaFair sales office is the volume of orders generated by each salesperson. Last year, the overall company average was $417,330 with a standard deviation of $45,285. (Hint: The finite population correction factor, Equation 7.5, is required.) a. Determine the probability the sample of 40 will have a sales average less than $400,000. b. What shape do you think the distribution of all possible sample means of 40 will have? Discuss. c. Determine the scale of the standard deviation of the distribution of the sample mean of all possible samples of size 40. d. How would the answers to parts a, b and c change if the home office brought 60 salespeople to Orlando? Provide the respective answers for this sample size. e. Each year SeaFair invites the sales personnel with sales above the 85th percentile to enjoy a complementary vacation in Hawaii. Determine the smallest average salary for the sales personnel that were in Hawaii last year. (Assume the distribution of sales was normally distributed last year.) 7-54. United Manufacturing and Supply makes sprinkler valves for use in residential sprinkler systems. United supplies these valves to major companies such as Rain Bird and Nelson, who in turn sell sprinkler products to retailers. United recently entered into a contract to supply 40,000 sprinkler valves. The contract called for at least 97% of the valves to be free of defects. Before shipping the valves, United managers tested 200 randomly selected valves and found 190 defect-free valves in the sample. The managers wish to know the probability of finding 190 or fewer defect-free valves if in fact the population of 40,000 valves is 97% defect-free. Discuss how they could use this information to determine whether to ship the valves to the customer. 8-12. Allante Pizza delivers pizzas throughout its local market area at no charge to the customer. However, customers often tip the driver. The owner is interested in estimating the mean tip income per delivery. To do this, she has selected a simple random sample of 12 deliveries and has recorded the tips that were received by the drivers. These data are $2.25 $2.50 $2.25 $2.00 $2.00 $1.50 $0.00 $2.00 $1.50 $2.00 $3.00 $1.50 a. Based on these sample data, what is the best point estimate to use as an estimate to use as an estimate of the true mean tip per delivery? b. Suppose the owner is interested in developing a 90% confidence interval estimate. Given the fact that the population standard deviation is unknown, what distribution will be used to obtain the critical value? c. Referring to part b, what assumption is required to use the specifies distribution to obtain the critical value? Develop a box and whisker plot.

1. 7-32.
SeaFair Fashions relies on its sales force of 220 to do an initial
screening of all new fashion. The company is currently
bringing out a new line of swimwear and has invited 40
salespeople to its Orlando home office. An issue of constant
concern to the SeaFair sales office is the volume of orders
generated by each salesperson. Last year, the overall company
average was $417,330 with a standard deviation of $45,285.
(Hint: The finite population correction factor, Equation 7.5, is
required.)
a. Determine the probability the sample of 40 will have a sales
average less than $400,000.
b. What shape do you think the distribution of all possible
sample means of 40 will have? Discuss.
c. Determine the scale of the standard deviation of the
distribution of the sample mean of all possible samples of size
40.
d. How would the answers to parts a, b and c change if the home
office brought 60 salespeople to Orlando? Provide the
respective answers for this sample size.
e. Each year SeaFair invites the sales personnel with sales
above the 85th percentile to enjoy a complementary vacation in
Hawaii. Determine the smallest average salary for the sales
personnel that were in Hawaii last year. (Assume the
distribution of sales was normally distributed last year.)
7-54.
United Manufacturing and Supply makes sprinkler valves for
use in residential sprinkler systems. United supplies these
valves to major companies such as Rain Bird and Nelson, who
in turn sell sprinkler products to retailers. United recently
entered into a contract to supply 40,000 sprinkler valves. The
contract called for at least 97% of the valves to be free of

2. defects. Before shipping the valves, United managers tested
200 randomly selected valves and found 190 defect-free valves
in the sample. The managers wish to know the probability of
finding 190 or fewer defect-free valves if in fact the population
of 40,000 valves is 97% defect-free. Discuss how they could
use this information to determine whether to ship the valves to
the customer.
8-12.
Allante Pizza delivers pizzas throughout its local market area at
no charge to the customer. However, customers often tip the
driver. The owner is interested in estimating the mean tip
income per delivery. To do this, she has selected a simple
random sample of 12 deliveries and has recorded the tips that
were received by the drivers. These data are
$2.25 $2.50 $2.25 $2.00 $2.00 $1.50
$0.00 $2.00 $1.50 $2.00 $3.00 $1.50
a. Based on these sample data, what is the best point estimate to
use as an estimate to use as an estimate of the true mean tip per
delivery?
b. Suppose the owner is interested in developing a 90%
confidence interval estimate. Given the fact that the population
standard deviation is unknown, what distribution will be used to
obtain the critical value?
c. Referring to part b, what assumption is required to use the
specifies distribution to obtain the critical value? Develop a box
and whisker plot to illustrate whether this assumption seems to
be reasonably satisfied.
d. Referring to parts b and c, construct and interpret the 90%
confidence interval estimate for the population mean.

3. 8-38.
The Northwest Pacific Phone Company wishes to estimate the
average number of minutes its customers spend on long-distance
calls per month. The company wants the estimate made with
99% confidence and a margin of error of no more than 5
minutes.
a. A previous study indicated that the standard deviation for
long-distance calls is 21 minutes per month. What should the
sample size be?
b. Determine the required sample size if the confidence level
were changed from 99% to 90%.
c. What would the required sample size be if the confidence
level was 95% and the margin of error was 8 minutes?
8-56.
As the automobile accident rate increases, insurers are forced to
increase their premium rates. Companies such as Allstate have
recently been running a campaign they hope will result in fewer
accidents by their policyholders. For each six-month period
that a customer goes without an accident, Allstate will reduce
the customer’s premium rate by a certain percentage.
Companies like Allstate have reason to be concerned about
driving habits, based on a survey conducted by Drive for Life, a
safety group sponsored by Volvo of North America, in which
1,100 drivers were surveyed. Among those surveyed, 74% said
that careless or aggressive driving was the biggest threat on the
road. One-third of the respondents said that cell phone usage
by other drivers was the driving behavior that annoyed them the
most. Based on these data, assuming that the sample was a
simple random sample, construct and interpret a 95%

4. confidence interval estimate for the true proportion in the
population of all drivers who are annoyed by cell phone users.
Week 4 Homework Hints
Chapters 7, 8
Problem 7.32 General Background For Understanding This
Problem:
Note: this chapter’s z-score formula differs from the earlier z-
score formula on p. 227, formula 6.2, because this chapter is all
about finding the probability that a sample MEAN (“X-bar”)
differs from a population mean (U). The formula on p.227 finds
the probability that an INDIVIDUAL VALUE (X) differs from a
population or sample mean.)
Now, on p. 271, the authors state that the distance a given
sample mean is from the center of the distribution can be
determined using the z-value for the sampling distribution of
the sample mean: (formula 7.4)
We can use this to solve probability problems involving sample
means.
One other twist may be necessary: if the sample that you select
is relatively large compared to the population – that is, if n >
5% of N – then you can actually reduce the standard error of the
mean using the finite population correction factor; in this case,
the formula becomes: (formula 7.5, p. 271)
Specific Hints For Solving Problem 7.32:
Problem 7.32, a,b,c,:

5. For this problem, you will want to use formula 7.5 on p. 271.
Part a says “determine the probability that the random sample
of 40 will have a sales average less than $400,000. So we know
that “X-bar”, the sample mean, is 400,000. We also know that
n, the sample size = 40. We need to know what u, the
population mean is, and that’s given in the problem (“last year,
the overall company average was $417,330”). Now we also need
the “finite population correction factor” since the population
size (N) is a sales force of 220. The sample size (n) as we
already know is 40. The fpc is used when your sample size is
greater than 5% of your population size. So n/N = 40/220 =
.18,or 18%, so we need to use the fpc. The population standard
deviation (sigma) is also given to you. You should now have
everything you need to plug into the equation and calculate your
z-score. Once you calculate the z-score, you need to go to the
normal table and look up the appropriate area under the curve
(or use the Excel function NORM.S.DIST, plug in your z-score,
put “TRUE” in the “Cumulative” box). Remember, your z-score
will be negative, and you’re looking for the area under the
curve (the probability) of getting a sales average LESS than
$400,000….so you’re looking for the area under the curve to the
left of that value.
For 7.32 b, review the discussion of the Central Limit Theorem
in the chapter (see Theorem 3 on p. 268).
For 7.32c, the “standard deviation of the distribution of sample
means” is also called the “standard error” (see Theorem 2 on
p.267). Hint: this is equivalent to the denominator of the
formula you used to solve problem 7.32a.
Problem 7-54, to be clear, requires a probability calculation,
even though the last line in the problem states “Discuss how
they could use this information…..”. We want to use the
formula for proportions, just like we used a formula for sample

6. means in the prior problem. The formula to be used when
trying to find the probability of getting a sample proportion of a
certain size, when you know the population proportion and
sample size, is shown below…see also the examples on pp.282-
285; here, p is the same as p-bar (sample proportion), and p in
the formula below is the same as the “pie” symbol,, which is the
population proportion. In this problem, the managers tested a
simple random sample of n = 200 sprinkler valves from the
population and found x = 190 defect-free valves. So the sample
proportion is:
190
0.95
200
x
p
n
===
This is less than the required 0.97 for the population, which is
your P.
n
p)
p(1
p
p
σ
p
p
z
p
-
-

7. =
-
=
Once you get your calculated z score from the formula above,
determine the probability of getting that z-score (or less) by
using the Excel function Norm.S. Dist and plugging in your z
score, putting “TRUE” in the cumulative box:
Problem 8-12:
For this problem, pay particular attention to pages 304-310. A
good example to follow is Example 8-3 on p. 309. You can use
the Excel function “Confidence.T” to determine the margin of
error. To create the actual confidence interval, you subtract the
margin of error from the mean to get the lower end, and then
add the margin of error to the mean to arrive at the upper end.
Of course, you will need to calculate the mean and standard
deviation once you have your data in a single column. Please
remember that you do not have to construct a box and whisker
plot that is mentioned in part c of the problem. To use the
Confidence.T function, you need to input:
· the alpha level (so, for example a 90% confidence level would
require an alpha of .10, a 99% confidence level would require
and alpha of .01, etc.)
· the standard deviation
· the sample size
Problem 8-38 part a only:
Part a says “A previous study indicated that….for (all) long
distance calls”, so assume we know the population standard

8. deviation, or sigma. You can use the formula on p. 315
(equation 8.6) to manually calculate this, or you can simply
create the formula in Excel by plugging in the values for z,
sigma, and e, then squaring.
The formula to use is shown below:
Problem 8-56:
The formula for the confidence interval around a proportion is
covered on p. 322, formula 8.10. You can do this manually, or
create a simple Excel formula to plug in the values. The actual
formula to use is listed on the slide immediately below; an
example of how to calculate this can be found in the second
slide:
_1423049312.unknown