Answer to Question #292506 in Statistics and Probability for rox

Question

In 2018, the braking distance of Toyota Camry cars on a wet surface follows a normal distribution. Its mean is 122 feet with a standard deviation of 20 feet. What is the probability that a randomly selected Toyota Camry will have a braking distance of more than 130 feet?

Answer 1

Let $X=$ the braking distance:$X\sim N(\mu, \sigma^2).$

Given $\mu=122ft, \sigma=20ft.$

$$P(X>130)=1-P(X\le130)$$

$$=1-P(Z\leq\dfrac{130-122}{20})=1-P(Z\leq0.4)$$

$$\approx0.344578$$