A new Firestone tire is guaranteed to last for 40,000 miles. The actual mean life of the tires is 47,000 miles with a standard deviation of 4,000 miles.

a) What percent of the tires will last for at least 40,000 miles?
b) What percent of the tires will not last for at least 40,000 miles?
c) What is the probability that a tire will last for more than 50,000 miles?
d) The Firestone Company wants to advertise how long some of their tires last. They decide to state how long the top 3% of their tires will last. How many miles will the top 3% of their tires last?

Question

A new Firestone tire is guaranteed to last for 40,000 miles. The actual mean life of the tires is 47,000 miles with a standard deviation of 4,000 miles.

a) What percent of the tires will last for at least 40,000 miles?
b) What percent of the tires will not last for at least 40,000 miles?
c) What is the probability that a tire will last for more than 50,000 miles?
d) The Firestone Company wants to advertise how long some of their tires last. They decide to state how long the top 3% of their tires will last. How many miles will the top 3% of their tires last?

anonymous · Answer

You can use a normal distribution with a mean of 40,000.

This can be understood:

a) What percentages of the tires will lie above the mean?
b) What percentages of the tires will lie below the mean?
c) 50,000 - 40,000 = 10,000 miles. You need to convert 10,000 units of miles in chunks of standard deviations (sd). Once you find how many sd +10,000 lies, you need to find the percentages that lies above that.
d) You must go in the other way around: You must convert the %  into sd, and then to miles.

And you're done.