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

Answer 1

What are you doing here? Testing a hypothesis? Finding some probability?

Answer 2

what is the probability that a tire will not last 40,000 miles

Answer 3

\[P(X<40,000)=P\left(\frac{X-47,000}{4,000}<\frac{40,000-47,000}{4,000}\right)=P(Z<-1.75)\]
Consult a \(z\) table, like the one here: http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf