SOLUTION: I hope this is in the right category. The monthly salaries in a company with 5000 employees are normally distributed. The mean salary is $3100 with a standard deviation of $700

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Question 1074409: I hope this is in the right category.
The monthly salaries in a company with 5000 employees are normally distributed. The mean salary is $3100 with a standard deviation of $700. What percentage of employees earn more than $2400 per month? How many employees earn more than $2400 per month?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 3100
standard deviation is 700.

2400 is (3100 - 2400) / 700 = 1 standard deviation from the mean in a negative direction.

that makes the z-score equal to -1.

with z-scores, the mean is 0 and the z-score is the number of standard deviations away from the mean.

the formula is z = (x-m) / s

z is the z-score
x is the raw score
m is the mean
s is the standard deviation.

the formula becomes z = (2400 - 3100)/700 = -700/700 = -1

to find the percentage of employees that earn more than a z-score of -1, look up in the z-score table for a rate (rate = % / 100) to the left of a z-score of -1.

then take 1 minus that rate for a rate to the right of a z-score of -1.

if you used the table linked to below, you would have found the rate to the left of the z-score of -1 equal to .1587 and then gotten the rate to the right of the z-score of -1 equal to 1 - .1587 = .8413.

http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

alternatively use a calculator that goes normal distribution type problems.

i used the following calculator.

http://davidmlane.com/hyperstat/z_table.html

if allows me to find the rate to the left of or to the right of a particular z-score or in between 2 z-scores or outsides of 2 z-scores.

very nice calculator.

i got a rate of .8413

that means that 84.13% of the employees earn more than 2400 per month.

the number of employees that earn more than 2400 per month would be equal to 5000 * .8413 = 4206.5 which would be rounded to 4206 or 4207.

by convention of mathematical rounding rules, you would round to 4207.

the same calculator can be used with raw scores or z-scores.

with z-scores, mean is 0 and standard deviation is 1.

with raw scores, mean is 3100 and standard deviation is 700.

results are shown below:

$$$

$$$

the same calculator can be used to find the area from the z-score or the z-score from the area.

it can do the same using the raw mean score and standard deviation as well.

nice calculator.

even gives you a picture of the area under the distribution curve that it calculated for you.

use of the table rather than the calculator would have given you a result as shown below.

it's more work, but you get the same answer if you do it right.

$$$

$$$

the row heading would -1.0 and the column heading would be .00

add them together and you get a z-score of -1.00.