Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.5 years, and standard deviation of 3.4 years.

The 6% of items with the shortest lifespan will last less than how many years?

Answer 1

Here mean of he lifespan = $\mu$ = 14.5 years

standard deviation = $\sigma$ = 3.4 years

The 6% of items with the shortest lifespan will last less than let say x₀ years

so here

P(x < x₀) = 0.06

z = NORMSINV(0.06) = -1.5548

(x₀ - 14.5)/3.4 = -1.5548

x₀ = 9.214 years