Sorry if I'm wrong, not much of an expert either but I hope I help!

Decide if this 3% (0.03) should be on the extreme left or extreme right.

1.

(I concluded it should be extreme left of the normally distributed curve.)

2.Let X be max number of years for warranty. Which means you want to find, P(X<0.03)

3.Now find the area under the curve starting from the center (i.e. mean)

3.1.Area under the curve is 1. Area under curve starting from center is 0.5.

Therefore, 0.5 - 0.03 =0.47

3.2.Referring to the Z-table: The corresponding Z value for an area of 0.47 is 1.88. However you need to factor in this is on the left side of the standard normal curve, and need to add a negative sign to it. i.e. -1.88Given, Z=-1.88, mean= 35 and sigma(std dev)=8 substitute them into the formula X=mean+(Z * sigma)

4.

Ans:X = 35 + (-1.88 * 8) = 35 -15.04 = 19.96 ~ 20 years

The warranty period should be 20 years.

P.S. I'm so so sorry if I'm wrong. I just picked up stats again after a 2 year hiatus having to serve in the army so I'm kind of rusty!