An insurance company has a call center that makes cold calls

An insurance company has a call center that makes cold calls to individuals trying to sell life insurance. The probabilty of making a sale is 0.10. Assume binomial properties apply. If an individual in the center makes 20 calls, what is the probability they will make sales on more than 4 calls? a .9569 b. .0431 c. .2000 d. .0898

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < = 4) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 20 4 ) * 0.1^4 * ( 1- 0.1 ) ^16 + ( 20 3 ) * 0.1^3 * ( 1- 0.1 ) ^17 + ( 20 2 ) * 0.1^2 * ( 1- 0.1 ) ^18 + ( 20 1 ) * 0.1^1 * ( 1- 0.1 ) ^19 + ( 20 0 ) * 0.1^0 * ( 1- 0.1 ) ^20
= 0.957
P( X > 4) = 1 - P ( X <=4) = 1 -0.957 = 0.0431

ANS ) b. .0431