Ch 5, 6, 7 Questions 5

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.5 years, and standard deviation of 3.2 years.

If you randomly purchase one item, what is the probability it will last longer than 21 years?

Round answer to three decimal places

Answer 1

Since this is normally distributed, we'll need to find the z score for 21 years.

This uses the formula z = ^(X-µ)/_σ.

z = (21-12.5)/3.2 ≈ 2.656. You can now either plug this into a calculator or into a table.

P(X>21) = P(Z>2.656)

= 0.0039 or 0.39% (from the table with z = 2.66)

= 0.00395 or 0.395% (from the calculator)

Since we're rounding to 3 decimal places, we find that the probability of the purchased item lasting longer than 21 years is 0.004 or 0.4%.