1. The ages of customers at a store are normally distributed with a mean of 45 years and a standard deviation of 13.8 years. (a) What is the z-score for a customer that just turned 25 years old? Round to the nearest hundredth.
(b) Give an example of a customer age with a corresponding z-score greater than 2. Justify your answer.

Part (a)

The raw score is x = 25. The mean and standard deviation are mu = 45 and sigma = 13.8 respectively.

The z score is computed with the formula below

z = (x-mu)/sigma

z = (25-45)/13.8

z = -1.449275 approximately

z = -1.45 is the final answer

Part (b)

We want the z score to be larger than 2. So z > 2.

This is the same as wanting the expression (x-mu)/sigma to be larger than 2

(x-mu)/sigma > 2

(x-45)/13.8 > 2

x-45 > 2*13.8

x-45 > 27.6

x > 27.6+45

x > 72.6

If a customer's age is greater than 72.6 years, then this means they have a z score greater than 2. We can say they are more than 2 standard deviations above the mean.

If you need a whole number, then I'd round up to 73. Or you could pick any age larger than this.

v: l•w•h÷2.

v: 20•6•8 ÷2

v: 960÷2

v: 480