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# Confidence intervals and hypothesis testing? Maybe?

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A local merchant is interested in obtaining a small business loan to expand his business. He will be able to obtain a more favorable 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?

Use one of the following to address
-Confidence intervals and hypothesis testing
-Decision trees (and their use in solving managerial problems),
-Critical fractile analysis (and its use in determining optimal demand levels),
-Analysis of variance/ANOVA (and its use in understanding differences between group means),
-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),
-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and
-Optimization modeling (and its use in determining the best solution given a set of constraint).

How to approach this? Help!!!!!!

##### Solution Summary

The solution addresses a local merchant is interested in obtaining a small business loan to expand his business. He will be able to obtain a more favorable 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?

Use one of the following to address
-Confidence intervals and hypothesis testing
-Decision trees (and their use in solving managerial problems),
-Critical fractile analysis (and its use in determining optimal demand levels),
-Analysis of variance/ANOVA (and its use in understanding differences between group means),
-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),
-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and
-Optimization modeling (and its use in determining the best solution given a set of constraint).

##### Solution Preview

This is a normal distribution problem:
<br>His average revenue is 13000, and standard deviation is 2500
<br>Then we are to find the probability that next ...

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