Topten is a leading source on energy-efficient products. Their list of the top f
ID: 3289492 • Letter: T
Question
Topten is a leading source on energy-efficient products. Their list of the top four brands in terms of fuel efficiency for 2014 includes eleven Hondas.
Determine the probability distribution for the number of Hondas in a sample of three cars chosen from the top eleven. (Round your answers to 3 decimal places.)
What is the likelihood that in the sample of three at least one Honda is included? (Round your answer to 3 decimal places.)
Topten is a leading source on energy-efficient products. Their list of the top four brands in terms of fuel efficiency for 2014 includes eleven Hondas.
Explanation / Answer
a. There are n=11 cars, of which x=4 cars belong to Honda. Therefore, probbaility of success, p=x/n=4/11=0.36. The probability of success, p is constant through out the n number of trials. Assume, each trial is independent of another. Use binomial distribution to compute specific number of succeses, r in a sample of 3 cars. The formula is as follows:
P(X,r)=nCr(p)^r(1-p)^n-r
P(X=0)=3C0(0.36)^0(1-0.36)^3=0.262
P(X=1)=3C1(0.36)^1(1-0.36)^2=0.442
P(X=2)=3C2(0.36)^2(1-0.36)^1=0.249
b. P(X>=1)=P(X=1)+P(X=2)=0.442+0.249=0.691 (ans)