1) Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with a mean = 39

1) Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with a mean μ = 39 and standard deviation σ = 6. Use the TI-84 Plus calculator to answer the following.

(a) Find the 19th percentile of the tire lifetimes.

(b) Find the 71st 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

The 19th percentile of the tire lifetimes is __ thousand miles.

Part 2 of 4

The 71st 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.

2) A normal population has mean μ = 60 and standard deviation σ = 9. What is the 90th percentile of the population? Use the TI-84 Plus calculator. Round the answer to at least one decimal place.

The 90th percentile of the population is ___.

3) Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 12.5 pounds and standard deviation 5.1 pounds. Use the TI-84 Plus calculator to answer the following.

(a) What proportion of babies weigh more than 14 pounds?

(b) What proportion of babies weigh less than 16 pounds?

(c) What proportion of babies weigh between 11 and 15 pounds?

(d) Is it unusual for a baby to weigh more than 17 pounds?

Round the answers to four decimal places.