On average 45 percent of US beer drinkers order light beer 1

On average, 45 percent of U.S. beer drinkers order light beer.

1) What is the probability that none of the next eight customers who order beer will order light beer? (Round your answer to 4 decimal places.)

2) What is the probability that one of the next eight customers who order beer will order light beer? (Round your answer to 4 decimal places.)

3)What is the probability that two of the next eight customers who order beer will order light beer? (Round your answer to 4 decimal places.)

4)What is the probability that fewer than three of the next eight customers who order beer will order light beer? (Round your 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 = 0 ) = ( 8 0 ) * ( 0.45^0) * ( 1 - 0.45 )^8
= 0.0084

b)
P( X = 1 ) = ( 8 1 ) * ( 0.45^1) * ( 1 - 0.45 )^7
= 0.0548
c)
P( X = 2 ) = ( 8 2 ) * ( 0.45^2) * ( 1 - 0.45 )^6
= 0.1569
d)
P( X < 3) = P(X=2) + P(X=1) + P(X=0)   
= ( 8 2 ) * 0.45^2 * ( 1- 0.45 ) ^6 + ( 8 1 ) * 0.45^1 * ( 1- 0.45 ) ^7 + ( 8 0 ) * 0.45^0 * ( 1- 0.45 ) ^8   
= 0.2201