At a large company 75 of the employees use the direct deposi

At a large company, 75% of the employees use the direct deposit system for their paychecks. Suppose ten employees are randomly selected.

38. With the above setting find the probability that between 1 and 5 employees do NOT use direct deposit.

39. With the above setting find the probability that at least 9 employees use direct deposit.

40. With the above setting find the probability that less than 9 employees use direct deposit.

Solution

P(use direct deposit system)= 0.75
P(not use)= 0.25

38) P(ans) = p(1 not use ) + p(2 not use ) + p(3 not use ) + p(4 not use ) + p(5 not use )
                    = 0.25* 0.75^9    + 0.25*0.25 *0.75^8 + 0.25^3 * 0.75^7 + 0.25^4 * 0.75 ^6 + 0.25^5 * 0.75^5

(to solve put 0.75 =0.25 *3)
                   = 0.25^10 [ 3^9 + 3^8 + 3^7 + 3^6 + 3^5]
                  =0.25^10 * 29403 = 0.028041

39)    P (atleast 9 use ) = P(9 use ) + P(10 use) = 0.75^9 *0.25 + 0.75^10
                                          = 0.75^9 [0.25+0.75] = 0.075085

40)    P (less than 9 use) =1 - P (atleast 9 use) = 1- 0.075085 = 0.92491