Problem 80e

Given, Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5-mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

We have to find the middle 80% of her laps.

Step 1.

According to the given information, a random variable can be defined as, race times for randomly selected laps. And the distribution of her race times is normally distributed. So, follows Normal Distribution with a mean of 129.11 and a standard deviation of 2.28.

 

From area under the standard normal curve or Z table, 

, we have to find the a and b such that middle 80% of her laps.

 

So, 

 

and