Step-by-step explanation:
let's call X = speed of the cars on the expressway during rush hour.
the probability function is P(X).
mean = 68
SD = 55
P(X > 77) = P(X - mean > 77 - 68) =
= P((X - mean)/SD > (77 - 68)/55)
Z = (x - mean)/SD
(77 - 68)/55 = 9/55 = 0.163636364...
so,
P(X > 77) = P(Z > 0.163636364...) =
= 1 - P(Z <= 0.163636364...) ≈
≈ 1 - 0.565 (between 0.56356 and 0.56749) ≈
≈ 0.435
therefore, about 43.5% of the cars are traveling faster than 77 mph.
remember, while the probabilty distribution area is normed to 1, percentages are normed to 100.
so, % = probabilty × 100