Question

43​% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is​ (a) exactly​ three, (b) at least​ four, and​ (c) at most two. If​ convenient, use technology to find the probabilities.

P(3)=

Answer 1

Let , X be the number of adults who say cashews are their favorite nut .

p = 0.43%= 0.43 , n = 12

X is Binomial random variable with n = 12 and p = 0.43

a )

We have to find P(exactly​ three)

i.e P( x = 3 )

Using Excel function , =BINOMDIST( x , n , p , 0 )

P( x = 3 ) = BINOMDIST(3,12,0.43,0 ) = 0.1111

The probability that the exactly​ three adults who say cashews are their favorite nut is​ 0.1111

b)

We have to find P(at least​ four )

i.e P( x >= 4 )

P( x >= 4 ) = 1- P( x <= 3 )

Using Excel function , =BINOMDIST( x , n , p , 1 )

P( x <= 3 ) = BINOMDIST( 3 , 12 , 0.43 , 1 ) = 0.167102

So , P( x >= 4 ) = 1 - 0.167102 = 0.8329

The probability that the at least 4 adults who say cashews are their favorite nut is 0.8329

c)

We have to find P( at most two )

i.e P( x <= 2 )

Using Excel function , =BINOMDIST( x , n , p , 1 )

P( x <= 2 ) = BINOMDIST( 2 , 12 , 0.43 , 1 ) = 0.056

The probability that the at most 2 adults who say cashews are their favorite nut is 0.056