Question

Camille's Seed Haven claims that 90% of its sunflower seeds will germinate. Suppose the company's claim is true. Seth buys a packet with 30 sunflower seeds from Camille's Seed Haven and plants them in his garden. What is the probability that exactly 23 seeds will germinate?

A. 0.9820
B. 0.0258
C. 0.0180
D. 0.9742
E. 0.9922

Answer 1

Answer: C. 0.0180

Explanation:

Let x be the binomial variable that represents the number of seeds will germinate with parameter

n= 30 (Number of trials)

p=0.90 (Probability of success in each event)

Binomial probability formula :

Probability of getting success in x trials :
`P(X=x)=^nC_xp^x(1-p)^(n-x)`

For x= 23 , we have

`P(X=23)=^(30)C_(23)(0.90)^(23)(0.10)^(7)\\\\=(30!)/(23!(30-23)!)(0.90)^(23)(0.10)^7`

Simplify

`P(x=23)=0.018043169424\approx0.0180`

Hence, the probability that exactly 23 seeds will germinate = 0.0180