Question

b. If one car is randomly chosen, find the probability that it is traveling more than 78 mph

Answer 1

Let $X$ be the speed for a randomly selected car: $X\sim N(\mu, \sigma^2).$

Given $\mu=79\ mph, \sigma=10\ mph.$

$$P(X>78)=1-P(X\le78)$$

$$=1-P(Z\le \dfrac{78-79}{10})=1-P(Z\le-0.1)$$

$$\approx0.5398$$