Tire lifetimes:The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean = 40 and standard deviation = 4

. Use the TI-84 Plus calculator to answer the following.

(a) Find the 23 rd percentile of the tire lifetimes.

(b) Find the 75 th percentile of the tire lifetimes.

(c) Find the first 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

2%

of the tires violate the guarantee?

Round the answers to at least two decimal places.

Part 1 of 4 fill in the blank

The 23 rd percentile of the tire lifetimes is thousand miles.

Part 2 of 4

The 75 th percentile of the tire lifetimes is thousand miles.

Part 3 of 4

The first quartile of the tire lifetimes is thousand miles.

Part 4 of 4

The company should guarantee thousand miles.