A company establishes a fund of $120,000 from which it wants to pay an amount C to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year, independent of any other employee.
Determine the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.
(i think this is a poisson dist.?) Give answer and show work/explanation
Determine the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.
(i think this is a poisson dist.?) Give answer and show work/explanation
-
we can use binomdist with n =20, p = 0.02
E[x] = 20*0.02 = 0.4, so we could work out the CDF starting with x= 1 onwards until it exceeds 0.99.
x CDF
1 0.9401
2 0.9929
ie the probability of 2 or fewer > 0.99 which means P[x≥3] < 0.01 or 1%
thus C max can be 120,000/2
ans: $ 60,000
------
E[x] = 20*0.02 = 0.4, so we could work out the CDF starting with x= 1 onwards until it exceeds 0.99.
x CDF
1 0.9401
2 0.9929
ie the probability of 2 or fewer > 0.99 which means P[x≥3] < 0.01 or 1%
thus C max can be 120,000/2
ans: $ 60,000
------
-
P[0] = .98^20 = .6676
P[1] = 20c1*.02*.98^19 = .2725
CDF for P[1] = P[<=1] =.6676+.2725 = .9401
P[1] = 20c1*.02*.98^19 = .2725
CDF for P[1] = P[<=1] =.6676+.2725 = .9401
Report Abuse