Answer to Question #341490 in Statistics and Probability for dee

Question

QUESTION II   

An insurance company found that 45% of all insurance policies are terminated before their maturity 

date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a 

Binomial experiment.

Required:

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

QUESTION III   

Answer 1

Let $X=$ the number of policies terminated:$X\sim Bin(n, p).$

Given $n=10, p=0.45, q=1-p=0.55$

a)

$$P(X=8)=\dbinom{10}{8}(0.45)^{8}(0.55)^{10-8}$$

$$=0.02288958944$$

b)

$$P(X\ge8)=P(X=8)+P(X=9)+P(X=10)$$

$$=\dbinom{10}{8}(0.45)^{8}(0.55)^{10-8}$$

$$+\dbinom{10}{9}(0.45)^{9}(0.55)^{10-9}$$

$$+\dbinom{10}{10}(0.45)^{10}(0.55)^{10-10}$$

$$=0.02739183926$$

c)

$$P(X\ge2)=1-P(X=0)-P(X=1)$$

$$=1-\dbinom{10}{0}(0.45)^{0}(0.55)^{10-0}$$

$$-\dbinom{10}{1}(0.45)^{1}(0.55)^{10-1}$$

$$=0.97674289875$$