Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 year ago

# Statistics probability - normal distribution questions?

For a car traveling 60 kilometers per hour (km/h), the distance required to brake to a stop is normally distributed, with mean of 20 meters and a standard deviation of 2.4 meters. Suppose you are traveling 60 km/h in a residential area and a car moves abruptly into your path at a distance of 20 m.

(a) If you apply your brakes, what is the probability that you will brake to a stop within

18m or less?

(b) What is probability that you will avoid collision?

How would I solve these?

Relevance

μ = 20

σ = 2.4

a) z(X=18) = (18-20)/2.4 = -0.8333

From the z-tables

P(z<-0.8333) = 0.2033

b) To avoid a collision X < 20 m

z = 0

P(z<0) = 0.5000

• Find the z-score

(18 - 20) / 2.4 = -2/2.4 = -10/12 = -5/6 = -0.833333

http://www.z-table.com/

0.2033, or 20.33% of the area lies to the left of 18. You have about a 20.33% chance of stopping in 18 meters or less

You need to stop in 20 meters or less and 50% of the graph lies to the left of the 20m mark on the curve. You have a 50% chance of avoiding the collision