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

Step-by-step 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 :

$P(X=45) = \ ^{550}C_{45}(0.07)^{45}(1-0.07)^{550-45}\\\\= \dfrac{550!}{45!505!}(0.07)^{45}(1-0.07)^{505}\\\\\approx0.03532$

Hence, the required probability = 0.03532