Question

Do you tailgate the car in front of you? About 40% 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 11 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 = 11.

(b) Compute the expected number of vehicles out of 11 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

r	P ( r )
0	0.0036
1	0.0266
2	0.0887
3	0.1774
4	0.2365
5	0.2207
6	0.1471
7	0.0701
8	0.0234
9	0.0052
10	0.0007
11	0

Part b)

Mean = n * P = ( 11 * 0.4 ) = 4.4

Part c)
Variance = n * P * Q = ( 11 * 0.4 * 0.6 ) = 2.64
Standard deviation = √(variance) = √(2.64) = 1.62