Stat question 6

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.2 years, and standard deviation of 1.6 years.

If you randomly purchase one item, what is the probability it will last longer than 6 years?

Answer 1

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.2 years, and standard deviation of 1.6 years. If you randomly purchase one item, what is the probability it will last longer than 6 years?

Mean = 7.2 years

Standard Deviation = 1.6 years

Calculate Z-score of 6 years:

Z(6) = (6-7.2)/1.6 = -0.75

Area under the Standard Normal Curve on left for Z = -0.75 = 0.2268

To get probability of life greater than 6 years, we have to subtract 0.2268 from 1.0000

Probability of life greater than 6 years is = 1.0000 - 0.2268 = 0.7732, equivalent to 77.32%