Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14 years, and standard deviation of 3.6 years.

If you randomly purchase one item, what is the probability it will last longer than 24 years?

Round answer to three decimal places

Answer 1

Explanation:

We can use the z-score formula to find the probability that an item will last longer than 24 years:

z = (x - mu) / sigma

where x is the value we want to find the probability for (24 years), mu is the mean (14 years), and sigma is the standard deviation (3.6 years).

z = (24 - 14) / 3.6 = 2.778

Using a standard normal distribution table or calculator, we can find the probability that a z-score of 2.778 or greater occurs.

The probability of z-score of 2.778 or greater is 0.002.

Therefore, the probability that a randomly purchased item will last longer than 24 years is 0.002 or 0.2% (rounded to three decimal places).