please help me!!!?

Question

Based on factory and field tests, a car company determines that the trouble-free mileage for their new model is normally distributed with a mean of 31,600 miles and a standard deviation of 16,200 miles. The car is marketed with a 60,000-mile guarantee. Determine the percentage of cars of this make the company should expect to repair due to malfunctioning before 60,000 miles.

please explain as you're solving. thank u very much

Answer 1

It's a normal distribution with mean 31600 and s.d. 16200.
So P(X < 60000) = P(Z < (60000-31600) / 16200)
= P(Z < 1.7531)
= 0.960 to 3 d.p.
So the company should expect to repair 96.0% of the vehicles within the warranty period.