8. A government agency has 6,000 employees. The employees were asked whether the
ID: 3154122 • Letter: 8
Question
8. A government agency has 6,000 employees. The employees were asked whether they preferred a four-day work week (10 hours per day), a five-day work week (8 hours per day), or flexible hours. You are given information on the employees' responses broken down by gender.
Male Female Total
4 days 400 500 900
5 days 1,300 1,400 2,700
Flexible 300 2,100 2,400
Total 2,000 4,000 6,000
a) What is the probability that a randomly selected employee is a man and is in favor of a four-day work week?
b) What is the probability that a randomly selected employee is female?
c) A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours.
d) What percentage of employees is in favor of a five-day work week?
e) Given that a person is in favor of flexible time, what is the probability that the person is female?
f) What percentage of employees is male and in favor of a five-day work week?
g) What does the probability information tell you about the employees
Explanation / Answer
a) What is the probability that a randomly selected employee is a man and is in favor of a four-day work week?
From the table,
P(M n 4) = 400/6000 = 0.066666667 [ANSWER]
b) What is the probability that a randomly selected employee is female?
From the table,
P(F) = 4000/6000 = 0.6666666667 [ANSWER]
c) A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours.
From the table,
P(Flex|F) = 2100/4000 = 0.525 [ANSWER]
d) What percentage of employees is in favor of a five-day work week?
From the table,
P(5) = 2700/6000 = 0.45 [ANSWER]
e) Given that a person is in favor of flexible time, what is the probability that the person is female?
From the table,
P(F|Flex) = 2100/2400 = 0.875 [ANSWER]
f) What percentage of employees is male and in favor of a five-day work week?
From the table,
P(M n 5) = 1300/6000 = 0.216666667 [ANSWER]
g) What does the probability information tell you about the employees?
We can see that 2/3 of the employees are females, and almost half of them are in favor of 5 day work week, and a close seocnd is flexible time. Only a few, around 15%, are in favir of 4 day work week.
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