Question

Suppose that the speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 6 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(_____,______)

b. If one car is randomly chosen, find the probability that it is traveling more than 69 mph. ________

c. If one of the cars is randomly chosen, find the probability that it is traveling between 67 and 72 mph. _______

d. 72% of all cars travel at least how fast on the freeway? ______ mph.

Answer 1

Answer

(A) given that mean = 68 and standard deviation = 6

we know that we write X ~ N(mean, sigma)

setting the values, we get

X ~ N(68,6)

(B) using normalcdf

setting lower = 69, upper= 999, mean = 68 and sigma = 6

we get

P(X>69) = normalcdf(69,999,68,6)

= 0.4338

(C)

using normalcdf

setting lower = 67, upper= 72, mean = 68 and sigma = 6

we get

P(67<X<72) = normalcdf(67,72,68,6)

= 0.3137

(D) Using invNorm(area, mean, sd)

setting area = 0.72

mean = 68 and sd = 6

we get

Required speed = invNorm(0.72,68,6)

= 71.50 (2 decimals) or 71.4970 (4 decimals)