the lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean U=40 and standard deviation O=5 . Use the TI-84 Plus calculator to answer the following.

Question

(a) Find the 18THth percentile of the tire lifetimes.

(b) Find the 70th percentile of the tire lifetimes.

(c) Find the third quartile of the tire lifetimes.

(d) The tire company wants to guarantee that its tires will last at least a certain number of miles. What number of miles (in thousands) should the company guarantee so that only 5% of the tires violate the guarantee?

Round the answers to at least two decimal places.

Answer 1

Let's use the TI-84 Plus calculator to solve each part of this problem.

(a) Find the 18th percentile of the tire lifetimes.

1. Press 2nd then VARS to access the DISTR menu.
2. Select invNorm(.
3. Enter the percentile (0.18 for the 18th percentile), the mean (40), and the standard deviation (5):

   invNorm(0.18, 40, 5)
   

4. Press ENTER.

The result will give you the 18th percentile in thousands of miles.

(b) Find the 70th percentile of the tire lifetimes.

1. Press 2nd then VARS to access the DISTR menu.
2. Select invNorm(.
3. Enter the percentile (0.70 for the 70th percentile), the mean (40), and the standard deviation (5):

   invNorm(0.70, 40, 5)
   

4. Press ENTER.

The result will give you the 70th percentile in thousands of miles.

(c) Find the third quartile of the tire lifetimes.

The third quartile is the same as the 75th percentile.

1. Press 2nd then VARS to access the DISTR menu.
2. Select invNorm(.
3. Enter the percentile (0.75 for the third quartile), the mean (40), and the standard deviation (5):

   invNorm(0.75, 40, 5)
   

4. Press ENTER.

The result will give you the third quartile in thousands of miles.

(d) The tire company wants to guarantee that its tires will last at least a certain number of miles so that only 5% of the tires violate the guarantee.

This corresponds to the 95th percentile (since we want to know the threshold below which 95% of the tires fall).

1. Press 2nd then VARS to access the DISTR menu.
2. Select invNorm(.
3. Enter the percentile (0.95), the mean (40), and the standard deviation (5):

   invNorm(0.95, 40, 5)
   

4. Press ENTER.

The result will give you the number of miles (in thousands) that the company should guarantee.

After performing these calculations on the TI-84 Plus calculator, you can round the results as necessary. However, since I don't have a calculator interface, please enter these commands to obtain numerical results for each part.