UNIVERSITY OF MINES AND TECHNOLOGY, TARKWA
END OF MODULE EXAMINATIONS, DECEMBER 2024
COURSE NO. : MBS/MBF/MBM/MBS 577
COURSE NAME : QUANTITATIVE METHODS
CLASS : MBTM I TIME: 3HRS
Name: __________________________________________ Index Number: _______________
Credit will be given to clarity of expression and presentation of results.
SECTION A
Answer ALL Questions from this section
1. Assume you are thinking about starting a Business Incubation Hub (scholarship secretariat to
provide funding for small business start-ups) in your hometown, which has a population of
about 10,000 business start-ups. You need to know how many start-ups would qualify for the
Hub, which requires a business plan score of at least 130 points. You realize that the business
plan score is normally distributed with a mean of 100 and a standard deviation of 15. Complete
the following.
a. Find the approximate number of start-ups in your hometown who are eligible for Hub
scholarship.
b. Is it reasonable to continue your quest for a Business Incubation Hub in your hometown?
c. What would be the minimum business plan score needed if you wanted to start an incubation
club that included only the top 1% of business plan scores?
2. What is an estimator? Explain the three key properties of a good estimator
3. Explain the following
a. Type I error
b. Type II error
c. Null hypothesis
d. Alternative hypothesis
4. A worker claims that the average salary of part-time workers in mine companies in the Tarkwa
Municipality is not more than $60 per day. A random sample of eight companies is selected,
and the daily salaries (in dollars) are shown. Is there enough evidence to support the worker’s
claim at α = 0.01?
60 56 60 55 70 55 60 55
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SECTION B
Answer ANY ONE question from this section
5. You are the chief analyst of an insurance company. The data represent a sample of the number
of home fires started by candles for the past several years. Find the 99% confidence interval for
the mean number of home fires started by candles each year.
5460 6090 6310 7160 8440 9930
6. The average annual number of jobs available for registered engineers is 103,900. If we assume
a normal distribution with a standard deviation of 8040, find the probability that
a. More than 100,000 jobs are available for registered engineers
b. More than 80,000 but less than 95,000 jobs are available for registered engineers
c. If the probability is 0.1977 that more than X amount of jobs are available, find the value of
X
7. A recent study of 28 randomly selected employees of a company showed that the mean of the
distance they travelled to work was 14.3 miles. The standard deviation of the sample mean
was 2.0 miles.
a. Find the 99% confidence interval of the true mean.
b. If a manager wanted to be sure that most of his employees would not be late, how much
time would he suggest they allow for the commute if the average speed were 30 miles per
hour?
Course Examiner: Kofi Kamasa, PhD
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