QA 233 (Basic
Business Statistics)
Practice Problems
III
- Chapter 4
Delta-Touch,
a regional auditing firm, has been hired to audit the books for the Crystal
Legends Marketing Research. Donna Rhodonda, Delta-Touch top auditor, has been
given this assignment. Crystal Legends, which has twenty-three clients of their
own, only wants a quick overview rather than a full-blown audit. Because of
this, Ms. Rhodonda decides to only audit the accounts for five randomly selected
Crystal Legends’ clients. The results of her audit are provided below:
|
Crystal
Legends’ Client
|
Number
of Correct Entries
|
Number
of Incorrect Entries
|
|
Dunwoody
Furniture Makers
|
1219
|
38
|
|
Hanson’s
Appliance Production
|
2436
|
112
|
|
Molly’s
Maid Service
|
844
|
11
|
|
Springfield
Dry Cleaners
|
1856
|
39
|
|
Kozy
Kennels
|
564
|
17
|
-
In
how many different ways could Ms. Rhodonda have selected five Crystal
Legends’ clients for her audit? Given these results, what is the
probability that Ms. Rhodonda would select Dunwoody
Furniture Makers, Hanson’s
Appliance Production, Molly’s
Maid Service, Springfield Dry
Cleaners, and Kozy Kennels
for her audit?
-
Using
the data collected by Ms. Rhodonda, what would you estimate to be the
probability of an incorrect
entry? What approach(es) are you using to assess this probability? Please
explain.
-
What
would you estimate to be the probability of an incorrect entry in Kozy
Kennels’ books? What kind of probability is this?
-
What
would you estimate to be the probability that an entry in Crystal legends’
books is drawn from a manufacturing organization (Dunwoody
Furniture Makers or Hanson’s
Appliance Production)?
-
What
would you estimate to be the probability that an entry in Crystal legends’
books is incorrect and drawn from Molly’s
Maid Service account entries?
-
If
an entry in Crystal legends’ books is drawn from Molly’s
Maid Service account entries, what would you estimate to be the
probability that the entry is incorrect?
-
What
would you estimate to be the probability of an incorrect entry in the books
of a service organization? Why is
this an estimate? Hint:
create a new contingency table with type of industry – service vs.
manufacturing represented by the rows and status of entry – incorrect or
correct represented by the columns. Use this resulting table to find the
answer to the question.
-
Do
the type of industry (service vs. manufacturing) and the status of an entry
in the books (correct or incorrect) appear to be independent? Please
explain. Hint: use the same
table you created for question 7 to find the answer to the question.
Deep-Six,
Inc. is a manufacturer of SCUBA equipment. One of their most popular products is
their Ultimate Depth Gauge, an important piece of equipment for
preventing nitrogen narcosis (excess nitrogen in the bloodstream caused by
spending too much time at too great a depth). Deep-Six claims that the Ultimate
Depth Gauge has only a one in ten million chance of failure. To gain this
level of reliability, the Ultimate Depth Gauge is actually comprised of
two depth gauges (a primary gauge and a backup gauge). One of the safety
features of the Ultimate Depth Gauge is a fail-safe indicator light that glows
when at least one of the gauges (primary or backup) has failed.
-
If
the probability that each gauge fails is 0.001, and failures of the two
gauges are independent, is Deep-Six's claim valid?
If not, how low would the probability of failure for the first gauge have to
fall before Deep-Six's claim would be valid?
-
What
is the probability that the fail-safe indicator light will come on during a dive?
-
Suppose
that, given the first gauge fails, the probability that the second gauge
fails is 0.01. Now what is the probability that the Ultimate
Depth Gauge fails (i.e., both the primary and backup depth gauges that
comprise the Ultimate Depth Gauge fail)?
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