This document contains 10 problems related to statistical analysis. Problem 1 asks the reader to calculate measures of central tendency and dispersion for hearing test results. Problem 2 asks for the 72nd percentile of roller coaster wait times. Problem 3 uses Chebyshev's theorem to determine bounds on life expectancy.

1. QNT 275 Week 2 Homework Problem Set Excel File
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1.
In a hearing test, subjects estimate the loudness (in decibels) of a sound,
and the results are: 69, 67, 71, 72, 65, 75, 68, 68, 83, 73, 68.
Calculate the measures of central tendency (Mean, median, mode) and
the measures of dispersion (range, standard deviation, variance).
2.

2. The local amusement park was interested in the average wait time at
their most popular roller coaster at the peak park time (2 p.m.). They
selected 13 patrons and had them get in line between 2 and 3 p.m. Each
was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
117, 123, 110, 117, 99, 120, 148, 118, 119, 120, 45, 130, 118
What is the 72d percentile?
3.
The average life of Canadian women is 73.90 years, and the standard
deviation of the life expectancy of Canadian women is 9 years. Based on
Chebyshev's Theorem, determine the upper and lower bounds on the

3. average life expectancy of Canadian women such that at least 95 percent
of the population is included if the sample size is 100 women.
4.
The local amusement park was interested in the average wait time at
their most popular roller coaster at the peak park time (2 p.m.). They
selected 13 patrons and had them get in line between 2 and 3 p.m. Each
was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes): 118, 121, 114, 116, 110, 120,
145, 118, 119, 121, 45, 135, 118.
Calculate the measures of central tendency (Mean, median, mode) and
the measures of dispersion (range, standard deviation, variance).
5.

4. The average lateness for one of the top airline companies is 10 minutes.
The variance of the lateness measure is calculated as 8. An airplane
arrived 12 minutes after the stated arrival time. Calculate the z-score for
the lateness of this particular airplane.
6.
According to a survey of the top 15 employers in a major city in the
Midwest, a worker spends an average of 400 minutes a day on the job.
Suppose the standard deviation is 20 minutes and the time spent is
approximately a normal distribution.
What are the times within which approximately 99.73 percent of all
workers will fall?
7.

5. Recently an advertising company called 200 people and asked them to
identify the company that was in an ad running nationwide. The
following results were obtained.
What percentage of those surveyed could not correctly recall the
company?
8.
A local electronics retailer recently conducted a study on purchasers of
large screen televisions. The study recorded the type of television and
the credit account balance of the customer at the time of purchase. They
obtained the following results.
What percentage of purchases were plasma televisions by customers
with the smallest credit balances?
9.

6. The following is a partial relative frequency distribution of grades in an
introductory statistics course.
Find the relative frequency for the B grade.
10
A CFO is looking at what percentage of a company's resources are spent
on computing. He samples companies in the pharmaceutical industry
and develops the following stem-and-leaf graph.
What would be the class length used in creating a frequency histogram?
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QNT 275 Week 3 Homework Problem Set Excel File
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1.

7. A survey is made in a neighborhood of 90 voters. 75 are Democrats and
15 are Republicans. Of the Democrats, 30 are women, while 7 of the
Republicans are women. If one subject from the group is randomly
selected, find the probability the individual is a male Republican.
2.
Container 1 has 8 items, 3 of which are defective. Container 2 has 5
items, 3 of which are defective. If one item is drawn from each
container, what is the probability that only one of the items is defective?
3.
A letter is drawn from the alphabet of 26 letters. What is the probability
that the letter drawn is a vowel?

8. 4.
A family has two children. What is the probability that both are girls,
given that at least one is a girl?
5.
If n = 29 and p = .6, then the standard deviation of the binomial
distribution is

9. 6.
Consider a Poisson distribution with an average of 4 customers per
minute at the local grocery store. If X = the number of arrivals per
minute, find the probability of more than 6 customers arriving within a
minute.
7.
An important part of the customer service responsibilities of a cable
company is the speed with which trouble in service can be repaired.
Historically, the data show that the likelihood is 0.70 that troubles in a
residential service can be repaired on the same day. For the first four
troubles reported on a given day, what is the probability that all four will
be repaired on the same day?

10. 8.
Suppose that the waiting time for a license plate renewal at a local office
of a state motor vehicle department has been found to be normally
distributed with a mean of 29 minutes and a standard deviation of 6
minutes. Suppose that in an effort to provide better service to the public,
the director of the local office is permitted to provide discounts to those
individuals whose waiting time exceeds a predetermined time. The
director decides that 10 percent of the customers should receive this
discount. What number of minutes do they need to wait to receive the
discount?
9.
An apple juice producer buys all his apples from a conglomerate of
apple growers in one northwestern state. The amount of juice obtained
from each of these apples is approximately normally distributed with a
mean of 2.38 ounces and a standard deviation of 0.1 ounce. What is the
probability that a randomly selected apple will contain more than 2.40
ounces?
10

11. While conducting experiments, a marine biologist selects water depths
from a uniformly distributed collection that vary between 2.00 m and
8.00 m. What is the probability that a randomly selected depth is
between 2.25 m and 5.00 m?
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QNT 275 Week 4 Homework Problem Set Excel File
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1.
A sample of 100 items has a population standard deviation of 5.9 and a
mean of 32. Construct a 95 percent confidence interval for μ.
2.
At the end of 1990, 1991, and 1992, the average prices of a share of
stock in a portfolio were $34.75, $34.65, and $31.25 respectively. To

12. investigate the average share price at the end of 1993, a random sample
of 75 stocks was drawn and their closing prices on the last trading day of
1993 were observed with a mean of 33.78 and a standard deviation of
14.25. Estimate the average price of a share of stock in the portfolio at
the end of 1993 with a 90 percent confidence interval.
3.
A research study investigated differences between male and female
students. Based on the study results, we can assume the population mean
and standard deviation for the GPA of male students are µ = 3.3 and σ =
0.3. Suppose a random sample of 1200 male students is selected and the
GPA for each student is calculated. Find the interval that contains 90
percent of the sample means for male students.
4.
A manufacturing company measures the weight of boxes before
shipping them to the customers. If the box weights have a population
mean of 80 lb and standard deviation of 6 lb, respectively, then based on
a sample size of 100 boxes, what is the probability that the average
weight of the boxes will exceed 83 lb?

13. 5.
A random sample of size 100 is taken from a population with mean 64
and standard deviation 5.2. Find P(x bar < 60).