An insurance salesperson is able to sell policies to 15 of t

An insurance salesperson is able to sell policies to 15% of the people she contacts. Suppose she contacts 120 people during a 2- week period. a. What is the probability that she sells more than 20 policies? b. What is the expected number of policies she sells?

Solution

(a)Given X~Binomial(n=120, p=0.15)

P(X=x)=120Cx*(0.15^x)*(0.85^(120-x))

So the probability that she sells more than 20 policies is

P(X>20) = P(X=21)+P(X=22)+...+P(X=120)

=120C21*(0.15^21)*(0.85^(120-21))+...+120C120*(0.15^120)*(0.85^(120-120))

=0.2556828

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(b)expected number =n*p= 120*0.15 =18