SOLUTION: The average price of personal computers manufactured by MNM Company is $1,400 with a standard deviation of $250. Furthermore, it is known that the computer prices manufactured by

Algebra ->  Probability-and-statistics -> SOLUTION: The average price of personal computers manufactured by MNM Company is $1,400 with a standard deviation of $250. Furthermore, it is known that the computer prices manufactured by       Log On


   

Question 907665: The average price of personal computers manufactured by MNM Company is $1,400 with a standard deviation of $250. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed.
If 250 MNM computers were priced at or below $700.00, how many computers were produced by MNM?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
z = (x-m)/sd
x = 700 = price of 250 computers that were produced at that price or below.
m = 1400 = average price of all computers that were produced.
sd = 250 = standard deviation of all computers that were produced.

z = (x-m) / sd = (700 - 1400) / 250 = -700/250 = -2.8

z = -2.8

look up in the z-score table to see that a z-score of -2.8 has .00256 * area under the normal distribution curve to the left of it.

this means that .00256 of the computers were sold at a price at or below 700.

since there were 250 of them, then the total number of computers had to be 250 / .00256 = 100,000 computers were sold in all.

the actual answer you get will be determined by rounding.

some charts will show the area to the left of a z-score of -2.8 as .0026.

some calculators will be more accurate and show the z-score of -2.8 as .0025551906...

your answer will be somewhere around 100,000.

the z-score table i used is shown below:

https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf