Statistics question, please help asap?

Question

A Manufacturer that guarantees it's car for 80,000 km finds that 2.5% of the tires are returned under the warranty. Assuming a normal distribution with a standard deviation of 1250km, the mean life of the tires to the nearest kilometre is?

Answer 1

Prob (  X < 80000) = 2.5% = 0.025

 

Prob ( z < (80000 - mean)/1250 ) = 0.025

 

Prob ( z < -1.96) = 0.025 <--- per the normal table

 

(80000 - mean)/1250 = -1.96

 

80000 - mean = -1.96 * 1250

 

80000 - mean = -2450

 

mean = 82450