Question

The manager of a Finance Company has estimated that, because of a recession year, 7% of its 550 loan accounts will be delinquent. If the manager's estimate is correct, what is the probability that exactly 45 of the accounts will be delinquent

Answer 1

Answer: 0.03532

Explanation:

Given : p = 0.07 , n= 550

Binomial probability distribution:
`P(X=x)=\ ^nC_xp^x(1-p)^(n-x)`

The probability that exactly 45 of the accounts will be delinquent will be :

`P(X=45) = \ ^(550)C_(45)(0.07)^(45)(1-0.07)^(550-45)\\\\= (550!)/(45!505!)(0.07)^(45)(1-0.07)^(505)\\\\\approx0.03532`

Hence, the required probability = 0.03532