# Normal Distribution

Norm Dickins the town pharmacist is interested in obtaining a loan to expand his business. He will get a better interest rate if he can reasonably demonstrate that his near-term monthly revenues will be between $10,000 and $15,000. He doesn't know the exact level of sales to expect over the next several months, but based on past experience, he knows it should be around $13,000. He also knows that his sales vary by about $2,500 from month to month.

What is the probability that his store will generate the revenue required for him to obtain a favorable loan rate?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

We obtain the mean and standard deviation from the statement of the problem

M = 13000 =mean

s= 2500 =standard deviation

We assume normal distribution

x= z=(x-M )/s Cumulative probability corresponding to z

10000 -1.2 11.51% (From the tables or excel function)

15000 0.8 78.81% (From the tables or excel function)

Therefore the probability of the revenue being between 10000 and 15000 is 67.30% =0.7881-0.1151

Â© BrainMass Inc. brainmass.com October 6, 2022, 10:55 am ad1c9bdddf>https://brainmass.com/statistics/normal-distribution/11360