Net annual profits for small retail stores are normally distributed
with a mean of $60,000 and a standard deviation of $10,000.
If there are a total of 800 stores, how many would be expected to have
a profit of less than $37,000.

Hi!!

We will use the following table for calculations:
"Normal Distribution Table"
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/normaltable.html


We have a normal distributed ramdom variable X (Net annual profits)
with mean Mu = $60,000 and standard deviation StD = $10,000 .

We want to know how many would be expected to have a profit of less
than X=$37,000. So we need to find the probability for a store to have
profit of less than X.

The first step is to normalize the variable X:
Z = (X-Mu)/STD = (37,000-60,000)/10,000 = -2.3

Then:
P(X < 37,000) = P(Z < -2.3) =
              = 0.5 - P(0 < Z < 2.3) =
              = 0.5 - 0.4893 =
              = 0.0107

Then, it is expected that the 1.07% of the total number of stores have
a profit less than $37,000 .
We have a total population of 800 stores, and the 1.07% of them is
expected to have a profit less than $37,000, that is about 8 stores
from the total.


I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards.
livioflores-ga

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correct response. Highly recommended