Math 218
Final Exam
Spring 1998
I
NSTRUCTIONS
. Every numerical answer should be simplified to a fraction
or decimal. You must show your work and justify your methods to obtain full
credit. Use the continuity correction wherever it is appropriate. If you can’t
do one part of a problem but need that answer later, guess an answer and use
that guess for the later part. The exam is worth a total of 200 points.
Problem
1
.
(20 points) A company with 1,000 employees has the following
distribution of salaries for three age groups:
under 30 years
between 30 and 50
over 50 years
under $50,000
200
250
100
over $50,000
50
150
250
(a) Find the probability that a randomly chosen employee is at least 30
years old.
(b) Find the probability that a randomly chosen employee is under 30 given
the employee’s salary is over $50,000.
(c) Find the probability that a randomly chosen employee earns over $50,000
given the employee is under 30.
(d) Determine whether the events that a randomly chosen employee is “aged
under 30” and “earns over $50,000” are independent. Remember to jus-
tify your answer.
Problem
2
.
(20 points) In a certain country 3 out of every 50 inhabitants are
infected with malaria. A test is used to detect malaria; however the test is not
always accurate. For people without the disease the test gives a false result
1% of the time. For people with the disease the test gives a false result 2% of
the time.
(a) Draw the probability tree.
(b) Find the probability that a randomly selected inhabitant of the country
is not infected.
(c) Find the probability that a randomly selected inhabitant of the country
tests positive (i.e. the test indicates that the person has the disease.)
(d) Find the probability that a randomly selected inhabitant of the country
who tested positive is infected.
Problem
3
.
(20 points) A furniture retailer receives a shipment of sixteen so-
fas from a factory. Because inspection of each individual sofa is expensive
and time-consuming, the retailer has the policy of inspecting a random sam-
ple of six items from the shipment. The retailer will accept delivery of the
shipment if at most one sampled sofa in the shipment is defective.

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