1. THE UNIVERSITY OF LUSAKA
Assignment 1
(Due 22nd August 2012)
Question One
A group of female managers working for an insurance company have lodged a complaint with the
personnel department. While the women agree has the company has increased the number of female
managers, they assert that women tend to remain in lower level management positions when
promotions handed out. They have supported their argument by noting that, during the past 3 years,
only 8 of the 54 promotions awarded went to women. The personnel department has responded by
claiming that these numbers are misleading on two counts: First there are far fewer female managers
than male managers; second, many of the female managers have been hired during the past year, and
employees are virtually never promoted during their first year at the managerial level. The personnel
department has compiled the data shown in the table below in which managers who have been
employed for at least 1 year are classified according to gender and to promotion record. The
department claims that the decision to promote a manager (or not) is independent of the manager’s
gender. Would you agree?
Manager Promoted Not Promoted Total
Male 46 184 230
Female 8 32 40
Total 54 216 270
Question Two
(a) The quality control Department of a manufacturer has determined that 5% of the catalytic
converters produced by the company will be defective until an expensive overhaul is undertaken
two weeks from now. If a sample of three converters is randomly selected from next week’s
production, what is the probability distribution of the number of defective converters in the
sample?
(b) The table below shows a probability distribution for the random variable x .
(i) Compute E x , the expected value of x.
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(ii) Compute , the variance of x.
(iii) Compute , the standard deviation of x.
x 3 6 9
f x 0.24 0.49 0.27
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2. (c) A financial report showed that 35% of accountants are employed in public accounting.
Assume that this percentage applies to a group of 10 college graduates just entering the
accounting profession. What is the probability that at least three graduates will be
employed in public accounting?
(d) PC has observed that calculators fail and need to be replaced at the rate of three every
25 days.
a. What is the expected number of calculators that will fail in 30 days?
b. What is the probability that at least two will fail in 50 days?
c. What is the probability that exactly three will fail in 10 days?
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