Question

Weekly wages at a certain factory are

normally distributed with a mean of
of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makesbetween
$400 and $450.
[? ]%

Answer 1

The probability that a worker makes between $400 and $450 is .3413 using the calculator and .34 using the empirical rule.

Explanation:

There are two ways to approach this problem.

The first way is to find the z-score corresponding to $400 and $450 weekly wage and find the p-value in between these values.

• 
  `\displaystyle (400-400)/(50) < z < (450-400)/(50)`
• 
  `\displaystyle 0 < z < 1`

If you use the normalcdf function on your calculator and put 0 and 1 as the lower and upper bounds, respectively, you will get an area of .3413.

Another way of looking at this problem is to recognize that the weekly wages given are the mean and one standard deviation above the mean.

We can use the Empirical Rule, 68-95-99.7, in order to see that going one standard deviation above the mean would be an area of 68/2 = .34.

I've attached an image that shows you what the normal curve looks like.