Based on probability of normal distribution

Question

 Atire company wishes to set aminimum mileage guarantee on its new type of tire.Tests reveal that mean mileage is 67,900 with a standard deviation of 2050 miles and that the distribution miles follows the normal probability distribution.The company wants to set the minimum guaranteed mileage so that more 5 per cent of the tires will be replaced.What minimum mileage should the company announce?

Answer 1

What we need is 5% probability in lower tail.

z value  = -1.645

 

z value = (x - µ)/σ

-1.645 = ( x - 67900)/2050

x = 64527.75

 

So company should declare a mileage of 64528 miles.