Answer to Question #215784 in Statistics and Probability for Spencer

Question

A certain type of tomato germinates 90% of the time . A backyard farmer planted 25 seeds.
a. What is the probability that exactly 20 seeds germinate.
b. What is the probability that 20 or more seeds germinate
c. What is the mean number of seeds that germinate
d. Determine the variance and standard deviation in the number of seeds that germinate.

Answer 1

This is a binomial distribution with n=25, p=0.9.

a. $P(X=20)=C_{25}^{20}0.9^{20}(1-0.9)^{25-20}=0.0646.$

b. $P(X\ge20)=\sum_{i=20}^{25}C_{25}^i0.9^i(1-0.9)^{25-i}=0.9666.$

c. $\mu=np=25*0.9=22.5.$

d. $\sigma^2=np(1-p)=25*0.9*0.1=2.25.$

$\sigma=\sqrt{2.25}=1.5.$