Question

Q68 A branch of BNP-Paribas has an attractive credit programme. Customers meeting certain requirements can obtain a credit card called “BNP Wunder”. Local merchants in surrounding communities accept this card. The advantage is that with this card, goods can be purchased at a 2% discount and further, there is no annual cost for the card. Past data indicates that 35% of all card applicants are rejected because of unsatisfactory credit. Assuming that credit acceptance, or rejection, is a Bernoulli process, and samples of 15 applicants are made. [8 Marks] (a) Develop a probability histogram for this situation. (b) What is the probability that exactly three applicants will be rejected? (c) What is the probability that at least three applicants will be rejected? (d) What is the probability that more than three applicants will be rejected? (e) What is the probability that exactly seven applicants will be rejected? (f) What is the probability that at least seven applicants will be rejected? (g) What is the probability that more than seven applicants will be rejected?

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Answer 1

Define X=number of rejection out of 15 applicants.

Since the probability of rejection is 0.35, we have X~Binomial(15,.35) due to Bernoulli process assumption.

a)  

b) P(exactly three applicants will be rejected)=P(X=3)=0.1109624

c) P(at least three applicants will be rejected)=P(X>=3)=1-P(X<=2)=1-0.0617341=0.9382659

d) P(more than three applicants will be rejected)=P(X>3)=1-P(X<=3)=1-P(X=3)-P(X<=2)=1-0.1109624-0.0617341=0.8273035

e) P(exactly seven applicants will be rejected)=P(X=7)= 0.1319264

f) P(at least seven applicants will be rejected)=P(X>=7)=1-P(X<=6)=1-0.7548425=0.2451575

g) P(more than seven applicants will be rejected)=P(X>7)=1-P(X<=7)=1-0.8867689=0.1132311

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