Thread: Problem with mean and standard deviation

1. Problem with mean and standard deviation

A distributor of auto tires claims that 90% of its best brand of tires last more than 140, 000 Km. It has been shown that the lifetime of the tires of that brand has a normal distribution with mean 100, 000 Km and a standard deviation of 20, 000 Km. Is the vendor's claim accurate?

We have done very basic problems like this in class but none this extensive.

From this I know that μ = 100, 000 and σ = 20,000.

I know I need to set up an inwquality with

a ≤ [(x-100,000)/20,000] ≥ b

but I don't know what a and b are to be and where the 140,000 and 90% fit in?

Thank you

2. You need to solve for x where

$P\left(Z<\frac{x-100000}{20000}\right)=.9$

If x = 140000 the claim is correct.