Sandford Health Systems has 6,000 employees. The employees were asked whether th

Question

Sandford Health Systems 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 sex. Male Female Total Four days 300 600 900 Five days 1,200 1,500 2,700 Flexible 300 2,100 2,400 Total 1,800 4,200 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?

Explanation / Answer

following information has been given

(a) a. What is the probability that a randomly selected employee is a man and is in favor of a four-day work week?

here total 300 is male employes in favor of four days out of 6000 employe

so required probability=300/6000=1/20=0.05

(b.) What is the probability that a randomly selected employee is female?

there are 4200 female employes out of 6000 employes

required probability=4200/6000=7/10=0.7

(c) c. A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours.

P(flexible|female)=P(flexible and female)/P(female)=(2100/6000)/(4200/6000)=0.5

requied probability=0.5

here there are 2100 female employes who favors flxible out of 6000 employes

(d) What percentage of employees is in favor of a five-day work week?

required %=100*2700/6000=45%

e. Given that a person is in favor of flexible time, what is the probability that the person is female?

P(female|flexible)=P(female and flexible)/P(flexible)=(2100/6000)/(2400/6000)=0.875

requied prbability=0.875

f. What percentage of employees is male and in favor of a five-day work week?

required %=100*1200/6000=20%

Male Female Total four days 300 600 900 five days 1200 1500 2700 flexible 300 2100 2400 total 1800 4200 6000

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