
Jon S. answered 10/13/20
Patient and Knowledgeable Math and English Tutor
x = speed of car. x is normally distributed with mean = 95, SD = 14
want to find P(75 < x < 135)
convert x to standard normal using z-score = (x - mean)/SD = (x - 95)/14
so P(75 < x < 135) = P((75-95)/14 < z < (135-95)/14) =
P(-1.43 < z < 2.86) =
P(z < 2.86) - P(z < -1.43) =
0.9979 - 0.0764 = 0.9215