Statistics question

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13 years, and standard deviation of 1.3 years.

The 4% of items with the shortest lifespan will last less than how many years?

Give your answer to one decimal place.

Answer 1

Since the lifespan is normally distributed, we first find the z-score from the standard normal probability table that is associated with the 4th percentile (0.04 probability). That z-score is -1.75.

Let x be the lifespan associated with the 4th percentile.

The z-score = (x - mean) / standard deviation, where mean given as 13 and std dev given as 1.3.

-1.75 = (x - 13)/1.3. Solve for x.