Question

Do you tailgate the car in front of you? About 25% of all drivers will tailgate before passing, thinking they can make the car in front of them go faster. Suppose that you are driving a considerable distance on a two-lane highway and are passed by 9 vehicles.

(a) Let r be the number of vehicles that tailgate before passing. Make a histogram showing the probability distribution of r for r = 0 through r = 9.

(b)Compute the expected number of vehicles out of 9 that will tailgate. (Round your answer to two decimal places.)

(c) Compute the standard deviation of this distribution. (Round your answer to two decimal places.)

Answer 1

The random variable representing the number of vehicles that tailgate before passing follows binomilal distribution with .

The probability mass function of is

  

a) A histogram is plotted using R as given below.

R <- 0:9
P <- dbinom(R, 9, 0.25)
barplot(P,R, col = "skyblue" , ylab = "Density", xlab = "R", main= "Binomial Distribution")

b) The expected value of binomial random variable is .

c) The satandard deviation of binomial random variable is .