I need help with a problem from my statistics homework. I don't understand this...

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.4 years, and standard deviation of 1.7 years.

The 3% of items with the shortest lifespan will last less than how many years?

Answer 1

Find the z-score associated with a probability of 3% (0.03). That z-score = -1.88

z = (x - mean)/ std deviation, where x = life span associated with 3% or less, mean = 12.4 and standard deviation = 1.7.

-1.88 = (x - 12.4)/1.7 -> solve for x