Question

5.5 points] Eighty percent of the applications received for a particular credit card are ac- cepted. Among the next 15 applications (a) what is the probability that exactly 4 will be accepted? (b) what is the probability that all will be rejected? (c) what is the probability that fewer than 3 will be accepted? (d) Determine the expected number and the variance of the accepted applications

Answer 1

Ans:

Use binomial distribution with n=15 and p=0.80

P(x=k)=15C_k*0.80^k*(1-0.80)^15-k

a)

P(x=4)=15C₄*0.80⁴*(1-0.80)¹¹=0.00001

b)

P(all)=P(x=15)=0.80¹⁵=0.0352

c)

P(x<3)=P(x=0)+P(x=1)+P(x=2)

=0.0000+0.0000+0.0000

=0.0000

d)

Expected number=15*0.8=12

standard deviation=sqrt(15*0.8*0.2)=1.55