Question

For a car travelling 60 km per hour (kph), the distance required to brake to stop is normally distributed with mean of 20 meters and a standard deviation of 3 meters. Suppose you are travelling 60 kph in a residential area and a car moves abruptly into your path at a distance of 25 meters.

a) if you apply your brakes, what is the probability that you will brake to a stop within 18 meters or less?

b) if the only way to avoid a collision is to brake to a stop, what is the probability that you will avoid the collision?

Answer 1

a)

z=$\frac{x-sample \space mean }{standard \space deviation }$

sample mean=20

standard deviation=3

x=18

P(x$\le$ 18)=P(Z$\le$ $\frac{18-20}{3}$ )

P(Z$\le$-0.67)=0.2514

The probability of braking to stop within 18 meters or less is 0.2514.

b)

x=25

P(x$\le$ 25)=P(Z$\le$ $\frac{25-20}{3}$ )

P(Z$\le$1.67)=0.9525

The probability that you will avoid the collision is 0.9525.