Question:

The city of Durham recently commissioned a study on the level of rents paid by households living and renting housing there. The study was based on a census of all of the households that were renting their housing in the city. The mean rent for households living and renting in Durham was calculated as $742.

1. As part of the same study it was reported that 7.3% of households living and renting in Durham were paying rents less than $500 per month. Assuming that rent is normally distributed in Durham, calculate the standard deviation of rent paid by Durham households who were renting their housing.
2. It was also reported that 12.3% of households living and renting in Durham paid more than $1500 per month in rent. Again, assume that rent is normally distributed in Durham and calculate the standard deviation of rent paid by Durham households who were renting their housing.
3. Compare your answers to parts (a) and (b) and draw whatever conclusions are justified from the results of your calculations and this comparison. Be as explicit as possible.

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