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?