Question

Speeding on the I-5. Suppose the distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 70.4 miles/hour and a standard deviation of 4.5 miles/hour. Round all answers to four decimal places.

1. What proportion of passenger vehicles travel slower than 80 miles/hour?

2. What proportion of passenger vehicles travel between 73 and 79 miles/hour?

3. How fast do the fastest 8% of passenger vehicles travel?  miles/hour

4. Suppose the speed limit on this stretch of the I-5 is 70 miles/hour. Approximately what proportion of the passenger vehicles travel above the speed limit on this stretch of the I-5?

Answer 1

Let X denotes the vehicle speed of a randomly selected passenger traveling on the Interstate 5 Freeway (I-5) in California.

X ~ Normal(70.4, 4.5²)

a) The proportion of passenger vehicles travel slower than 80 miles/hour

2) The proportion of passenger vehicles travel between 73 and 79 miles/hour

3) To find x such that

4) The proportion of the passenger vehicles travel above the speed limit on this stretch of the I-5