8of people in a city eligible to donate blood actually do Yo

8%of people in a city eligible to donate blood actually do. You randomly select four eligible blood donors and ask them if they donate blood. Complete parts (a) through (c) below.

(a) Construct a binomial distribution for

n=4

and

p=0.08.

x   

P(x)

0

1

2

3

4

(Round to three decimal places as needed.)

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 = 0 ) = ( 4 0 ) * ( 0.08^0) * ( 1 - 0.08 )^4
= 0.716
P( X = 1 ) = ( 4 1 ) * ( 0.08^1) * ( 1 - 0.08 )^3
= 0.249
P( X = 2 ) = ( 4 2 ) * ( 0.08^2) * ( 1 - 0.08 )^2
= 0.033
P( X = 3 ) = ( 4 3 ) * ( 0.08^3) * ( 1 - 0.08 )^1
= 0.002

P( X = 4 ) = ( 4 4 ) * ( 0.08^4) * ( 1 - 0.08 )^0
= 0.000041 ~ 0