The Normal Distribution

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.2 years, and standard deviation of 2.3 years.

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

Give your answer to one decimal place.

Answer 1

Marcella,

You want to find the Z score that corresponds to a p of.03 (3%). You can look that up in a table of the area under the normal curve. I got Z=-1.881. Z=(X-mean)/sd where mean =12.2 years an sd=2.3 years.

Solving for X=12.2-1.881*2.3=7.9 yrs. So 3% of the items sold will last less than 7.9 years.

Jim