Question

Avoiding an accident while driving can depend on reaction time. Suppose that reaction time, measured from the time the driver first sees the danger until the driver gets his/her foot on the brake pedal, is approximately symmetric and mound-shaped with mean 1.5 seconds and standard deviation 0.17 seconds. Use the 68-95-99.7 rule to answer the following questions.

This web site 68-95-99.7 rule graphically depicts the 68-95-99.7 rule and may help with the following questions.

What percentage of drivers have a reaction time more than 1.84 seconds?

%
What percentage of drivers have a reaction time less than 1.33 seconds?
%
What percentage of drivers have a reaction time less than 1.67 seconds?

Answer 1

Solution :

Using Empirical rule,

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

P( - 3< X < + 3) = 99.7%

(a)

P(X > 1.84) = 2.5%

(b)

P(X < 1.33) = 16%

(c)

P(X < 1.67) = 84%