Question

Suppose that the speed at which cars go on the freeway is normally distributed with mean 74 mph and standard deviation 9 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 72 mph.

c. If one of the cars is randomly chosen, find the probability that it is traveling between 73 and 76 mph.

d. 90% of all cars travel at least how fast on the freeway?  mph.

Answer 1

a. Here it is given that distribution is normal with mean=74 and standard deviation=9

So distribution is

b. Here we need to find

As distribution is normal we can convert x to z

c.

d. Here we need to find x such that

So using z table we get

Hence

So