Question

A loan company knows that 5% of its loans will be delinquent. Of the company’s 400 loan accounts, what is the probability

Answer 1

Answer:

Step-by-step explanation:

Given that a loan company knows that 5% of its loans will be delinquent.

since each loan is independent of the other p , probability for any random loan to be delinquent is constant 0.05

X no of delinquent loan accounts is binomial with n =400 and p = 0.05

Since n is very large and also np = 20 and nq >5 we can approximate to normal

Mean = np = 20 :  Variance = npq = 19

Std dev = 4.36

X is N(1, 4.36)

With continuity correcton we calculate the prob

a) that exactly 25 accounts will be delinquent?

=$P(24.5$

b) that fewer than 30 accounts will be delinquent?

=P(X<29.5)

= 0.9854

c) more than 24 accounts will be delinquent

=P(X>24,5)

=0.1509