3. A government agency has 6000 employees. The employees were asked whether they

Question

3. A government agency has 6000 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 employee responses broken down by sex. a (0000 000 FemaleTotal 4 days 5 days Flexible Total Male 1200 10 1800 1500S 2100 4200.10 900S 2700 5 2400 | 6000 (a) Find the joint probability table and the marginal probabilities. What is the probability that a randomly selected employee is a man and is in favor of a four day work week? (b) (c) What is the probability that a randomly selected employee is female? A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours. (d) (e) What percentage of employees are in favor of a five day work week? ( Given that a person is in favor of flexible time, what is the probability that the person is female? What percentage of employees are male and in favor of a five day work week? (g)

Explanation / Answer

male = 0.3

female = 0.7

4-day = 0.15

5-days = 0.45

flexible = 0.4

b)

0.05 {just see the row 4-day and column male}

c)

female = 0.7

d)

P(flexible|female) = P(flexible and female)/P(female) = 0.35 /0.7 = 0.50

e)

5-days=0.45

hence 45%

f)

P(Female|flexible) = P(flexible and female)/P(flexible) = 0.35/0.4=7/8

g)

male and 5-days = 0.2

Please rate

male female 4-days 300 600 900 5-days 1200 1500 2700 flexible 300 2100 2400 1800 4200 male female 4-days 0.05 0.1 0.15 5-days 0.2 0.25 0.45 flexible 0.05 0.35 0.4 0.3 0.7

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