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)   (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
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