# Normal distribution percentage problem.

1. Apr 11, 2012

### MACHO-WIMP

1. The problem statement, all variables and given/known data
A company pays its employees an average wage of \$3.25 an hour with a standard deviation of sixty cents. If the wages are approximately normally distributed, determine
the minimum wage of the employees who are paid the highest 5%.

2. Relevant equations
z=(x-μ)/σ

3. The attempt at a solution
I did:
.95=((x-3.25)/.6) which equals .57=x-3.25
therefore x=3.82. I feel like I didn't do this correctly and I can't finish the rest of my homework if I don't know what I'm doing. Thanks.

Last edited: Apr 11, 2012
2. Apr 11, 2012

### tal444

Isn't that equation for standardizing your values? 95% has nothing to do with z-scores.

Last edited: Apr 11, 2012
3. Apr 11, 2012

### MACHO-WIMP

Oh, shoot, you're right. Well how would I find out what 95% of the wages cause I don't have the slightest clue.

4. Apr 11, 2012

### tal444

Your z-value is +-σ from the mean. What is 95% in terms of σ on a normal distribution? Also, do you use calculators to help you in your class? If you do, this question should be quite straightforward.

5. Apr 11, 2012

### Ray Vickson

If z_95 is the 95th percentile of the standard normal (which is available in tables or on some calculators) you need $$z_{95} = \frac{x-3.25}{0.6}.$$ Note: you should divide by 0.6 not 6, since 0.6 is the standard deviation in dollars.

RGV

6. Apr 11, 2012

### MACHO-WIMP

No, my teacher wants us only using this table she gave us.