Question

Suppose that 50% of all jobs executed by ABC company miss their deadline. Suppose we take a random sample of 20 jobs executed by ABC company. What is the probability that at least 10 of these will miss their deadline? You can assume X = # of jobs that miss their deadlines has a binomial distribution

Answer 1

Number of jobs executed in the random sample : n= 20

Probability that a job miss their deadline :p = 50/100 =0.5

q = 1-p = 1-0.5=0.5

X = # of jobs that miss their deadlines has a binomial distribution

Probability mass function of X

Probability that at least 10 of these will miss their deadline i.e P(X10)

P(X10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)

P(X=10)	0.176197
P(X=11)	0.160179
P(X=12)	0.120134
P(X=13)	0.073929
P(X=14)	0.036964
P(X=15)	0.014786
P(X=16)	0.004621
P(X=17)	0.001087
P(X=18)	0.000181
P(X=19)	0.000019
P(X=20)	0.000001
Total	0.588099

P(X10)

= P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)

= 0.588099

Probability that at least 10 of these will miss their deadline = 0.588099