21 of adults would pay more for environmentally friendly pro

21% of adults would pay more for environmentally friendly products. You randomly select 10 adults. Find the probability that the number of adults who would pay more for environmentally friendly products is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.

(a)P(2)=

(Round to the nearest thousandth 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

a)
P( X = 2 ) = ( 10 2 ) * ( 0.21^2) * ( 1 - 0.21 )^8
= 0.3011
b)

P( X < 2) = P(X=1) + P(X=0)   
= ( 10 1 ) * 0.21^1 * ( 1- 0.21 ) ^9 + ( 10 0 ) * 0.21^0 * ( 1- 0.21 ) ^10
= 0.3464
P( X > = 2 ) = 1 - P( X < 2) = 0.6536

c)
P( X = 3 ) = ( 10 3 ) * ( 0.21^3) * ( 1 - 0.21 )^7
= 0.2134
P( X = 4 ) = ( 10 4 ) * ( 0.21^4) * ( 1 - 0.21 )^6
= 0.0993
P( X = 5 ) = ( 10 5 ) * ( 0.21^5) * ( 1 - 0.21 )^5
= 0.0317
P(2 <= X <= 5) = P( X = 2 ) + P( X = 3 ) + P( X = 4 ) + P( X = 5 ) = 0.3011 + 0.2134 + 0.0993 + 0.0317 = 0.6455