Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months 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?

2 Answers

Relevance
  • Mike G
    Lv 7
    6 months ago
    Favorite Answer

    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

    • Login to reply the answers
  • 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

    • Login to reply the answers
Still have questions? Get your answers by asking now.