Sampling Distributions?

Although cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 67% of vehicles on the roads in Winnipeg during rush hour are occupied by just the driver.





(a) If you choose 11 vehicles at random, what is the probability that 7 carry just the driver?





(b) If you choose 11 vehicles at random, what is the probability that at least 9 carry just the driver?





(c) If you choose 11 vehicles at random, the mean number of vehicles that carry just the driver is _______ and the standard deviation is _______











Please Stats pros i need your help. I will choose best answer!

Sampling Distributions?
The number of vehicles that carry just the driver, X, follows a binomial distribution with parameters p=0.67 and n=11.





E(X) = np


V(X) = np(1-p)


sd(X) = sqrt(np(1-p))


P(X=x) = n!/(x!(n-x)!) p^x (1-p)^(n-x)





Using these formulae:





(a) P(X=7) = 0.2372





(b) P(X%26gt;=9) = P(X=9) + P(X=10) + P(X=11) = 0.2413





(c)


mean = np = 11(0.67) = 0.737 or 7.37 vehicles


sd = sqrt(np(1-p)) = sqrt(11(0.67)(0.33)) = 1.5595 approx.