Dilbert forgot to study for the multiple-choice exam. Each question has four choices and there are 50 questions. Dilbert, in his infinite wisdom, decides to randomly guess on each problem. Find the probability for each:
a) If Dilbert gets 30 or more right, he will be named the company CEO.
b) If Dilbert gets 20 to 29 right, he will be promoted and get a 10% raise.
c) If Dilbert gets 10 to 19 right, he will get to keep his menial job and pay.
d) If Dilbert gets less than 10 right, he will be kicked out of cubicle central and unemployed
P(x) = 50Cx *0.25^x *0.75^(50-x)
a. P(30 <= x <= 50) = 1.642286e-7
b. P(20 <= x <= 29) = 0.01391744
c. P(10 <= x <= 19) = 0.8223985
d. P(0 <= x<= 9) = 0.1636839