Question

Because of economic conditions, a firm reports that 30 percent of its accounts Receivable from other business firms are overdue, if an accountant takes a random sample of 5 such accounts, determine the probability of each of the following case:
a) none of the accounts are overdue
b) exactly two accounts are overdue
c) most of the accounts are overdue
d) exactly 20 percent of the accounts are overdue

Answer 1

This is the binomial distribution with $p=0.3, \;\;n=5.$

a) $P(X=0)=C_5^50.3^0(1-0.3)^5=0.1681.$

b) $P(X=2)=C^2_50.3^2(1-0.3)^3=0.3087.$

c) $P(X\ge3)=P(X=3)+P(X=4)+P(X=5)=C^3_50.3^3(1-0.3)^2+$

$+C^4_50.3^4(1-0.3)^1+C^5_50.3^5(1-0.3)^0=0.1638.$

d) $P(X=5*0.2)=P(X=1)=C^1_50.3^1(1-0.3)^4=0.3602.$