Question

When completing a survey of 8 different companies, you find there is a 70% chance that a given company will offer an employee 4 weeks of vacation time after 10 years of service.

a. What is the probability that anywhere from 3 to 5 of the 8 companies you surveyed will offer an employee 4 weeks of vacation time after 10 years of service?

b. What is the probability that less than 4 of the 8 companies you surveyed will offer an employee 4 weeks of vacation time after 10 years of service?

c. What is the probability that exactly 7 of the 8 companies you surveyed will offer an employee 4 weeks of vacation time after 10 years of service?

Answer 1

Let , X be the number of companies who will offer an employee 4 weeks of vacation time after 10 years of service.

Here , X has a binomial distribution with parameter n=8 and p=70%=0.70

Therefore , the probability mass function of X is ,

; x=0,1,2,...........,n and q=1-p

= 0 ; otherwise

a. Now , If 3 and 5 are exclusive , then   ; From the binomial probability table

Therefore , the probability that anywhere from 3 to 5 of the 8 companies you surveyed will offer an employee 4 weeks of vacation time after 10 years of service is 0.1361

If 3 and 5 are inclusive , then  

; From the binomial probability table

Therefore , the probability that anywhere from 3 to 5 of the 8 companies you surveyed will offer an employee 4 weeks of vacation time after 10 years of service is 0.4369

b. Now ,

; From the binomial probability table

Therefore , the probability that less than 4 of the 8 companies you surveyed will offer an employee 4 weeks of vacation time after 10 years of service is 0.0580.

c) Now , P(X=7) = 0.1976 ;  From the binomial probability table

Therefore , the probability that exactly 7 of the 8 companies you surveyed will offer an employee 4 weeks of vacation time after 10 years of service is 0.1976.