Do you tailgate the car in front of you? About 40% of all drivers will tailgate

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 6 vehicles.

(b) Compute the expected number of vehicles out of 6 that will tailgate. (Round your answer to two decimal places.)
2 vehicles

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

Explanation / Answer

b)

p=.4

E(x) = [ 1*(.4*(6/64) + 2*(.4*15/64) + 3*(.4*20/64) + 4*(.4*15/64) + 5*(.4*6/64) + 6*(.4*1/64) ]

= (.4)*(1/64)*[6+30+60+60+30+6] = 1.2

c) E(x^2) = [ 1*(.4*(6/64) + 4*(.4*15/64) + 9*(.4*20/64) + 16*(.4*15/64) + 25*(.4*6/64) + 36*(.4*1/64) ]

= (.4)*(1/64)*[1+60+180+240+150+36] = 4.17

SD = sqrt(4.17-(1.2^2)) = sqrt(4.17-1.44) = 1.65

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.