X = wage

(a) `Z_1=(2.75-3.25)/0.6=-0.83333 `

`Z_2=(3.69-3.25)/0.6=0.73333`

So

`P(2.75<X<3.69)`

`=P(-0.833<Z<0.733)`

`=0.298+0.268`

`=0.566`

So about `56.6%` of the workers have wages between `$2.75` and `$3.69` an hour.

You can see this portion illustrated in the standard normal curve below.

12345$2.753.69Open image in a new page

The normal curve with mean = 3.25 and standard deviation 0.60, showing the portion getting between $2.75 and $3.69.

(b) W = minimum wage of highest `5%`

`z = 1.645` (from table)

`(x-3.25)/0.6=1.645`

Solving gives: `x = 4.237`

So the minimum wage of the top `5%` of salaries is `$4.24`.

In the graph below, the yellow portion represents the 45% of the company's workers with salaries between the mean ($3.25) and $4.24. (This is 1.645 standard deviations from the mean.)

The light green shaded portion on the far right representats those in the top 5%.

12345$3.254.24Open image in a new page

The right-most portion represents those with salaries in the top 5%.