According to a report from the Center for Studying Health Sy

According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal, June 26, 2008). Suppose eight individuals are randomly selected.

What is the probability that no more than two will delay or go without medical care? (Round your intermediate calculations and final answer to 4 decimal places.

What is the probability that at least seven will delay or go without medical care? (Round your intermediate calculations and final answer to 4 decimal places.)

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

a)
P( X < = 2)   = P(X=2) + P(X=1) + P(X=0)        
=   ( 8   2 ) * 0.2^2 * ( 1- 0.2 ) ^6 + ( 8   1 ) * 0.2^1 * ( 1- 0.2 ) ^7 +
( 8   0 ) * 0.2^0 * ( 1- 0.2 ) ^8   = 0.7969

b)
P( X = 7 ) = ( 8 7 ) * ( 0.2^7) * ( 1 - 0.2 )^1
= 0.0001
P( X = 8 ) = ( 8 8 ) * ( 0.2^8) * ( 1 - 0.2 )^0
= 0

P( X > = 7 ) =P( X = 7 ) + P( X = 8 ) = 0.0001