A human resource manager has classified....... A human resource manager has clas

Question

A human resource manager has classified.......

A human resource manager has classified the employees of the company firm according to their record of absenteeism last year and according to whether or not they were smokers. It was found that 28% of the employees smoked. Among the smokers. 70% were absent from work for more than 10 days last year. Among non-smokers. 90% were absent from work 10 or fewer days last year. Draw a well-labeled tree diagram using the information provided. What is the probability that a randomly chosen employee did not smoke? What is the probability that an employee did not smoke and w as absent 10 or fewer days? What is the probability an employee was absent more than 10 days last year? Knowing that an employee was absent 10 or fewer days, what is the probability that the employee was a smoker? Is the rate of absenteeism independent from whether an employee smokes? Justify your answer mathematically.

Explanation / Answer

let probability of smokers =P(S) and non smokers =P(NS)

and probabilty of absent more then 10 days =P(A) and absent for fewer then 10 days =P(NA)

1) decision tree

b) proabbailty that employee did not smoke =P(NS)=1-P(S) =1-0.28=0.72

c)probabilty =P(NSnNA) =0.72*0.9=0.648

d)probabilty P(A) =P(S)*P(A|S)+P(NS)*P(A|NS) =0.28*0.7+0.72*0.1=0.268

e)as Probabilty of absent for 10 or fewer days =P(NA) =1-P(A) =1-0.268 =0.732

hence required probabilty P(S|NA) =P(S)*P(NA|S)/P(NA) =0.28*0.3/0.732=0.114754

f) as P(A)=0.732

and P(S) =0.28

also P(AnS) =0.196

P(A)*P(S)= 0.732*0.28=0.20496 which is not equal to P(AnS) hence not independent.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.