ISOM 111 L7-L8, Fall 2010
1
Homework 1
Due: Monday, Sep 27, 4:00pm
Submit to the “Homework Collection Box, ISOM 111 L7-L8” outside Room 4351
I
. An insurance agency is examining the dollar amount of claims from clients who have home-
owners insurance. For the 900 people who ﬁled claims, the ﬁve-number summary of the amount is:
($8800, $8850, $8900, $9100, $9940).
(a) Would the histogram displaying the data for the 900 claims be nearly bell-shaped? If so, explain
how the summary indicates this. If not, determine if the data is skewed left or skewed right, and
explain how the summary indicates this.
(b) Would the boxplot for the data indicate any outliers? Explain why or why not.
II.
A drug manufacturer has hundreds of sales representatives all over the United States. A
histogram for yearly sales totals for each representative is roughly bell shaped and symmetric except
for 4 high outliers corresponding to representatives in Boston, MA. Their sales totals are at least
$60,000 greater than the next highest total. One analyst suggests dropping these 4 totals from the
data to get a better summary of the sales across all regions of the country.
(a) If the outliers were to be dropped, which measure of central tendency of the data set would be
aﬀected the most – the mean, the median, or the mode? Explain why.
(b) The high outliers are dropped from the data and the mean is determined to be $70,000 with
a standard deviation of $8,000. For future analysis, management would like to be able to identify
sales amounts that are “unusually low”, which they deﬁned as being among the lowest 2.5% of
all sales amounts. Using the Empirical Rule for this data, what amount should be considered the
cut-oﬀ for sales amounts being classiﬁed as unusually low?
III.
In order to control costs, a company wishes to study the amount of money its sales force
spends entertaining clients. The following is a random sample of six entertainment expenses (dinner
costs for four people) from expense reports submitted by members of the sales force.
$157
$132
$109
$145
$125
$139
(a) Calculate the sample mean ¯
x
and sample variance
s
2
.
(b) Assuming that the distribution of entertainment expenses is approximately normally dis-