Question

Hadey is approaching the housing situation from a different direction. He does a little research and learns that the mean rent for a one bedroom one bathroom apartment in Avocado Park is $1050 per month with a standard deviation of $125 per month.

A. The Avocado Park Housing Authority defines affordable housing as costing LESS than $900 per month for a 1B1R. Would such an apartment be considered unusual for the neighborhood?

B. Hadey wants to develop a new apartment building in Avocado Park offering 1B1R units at a price of $1000 per month. What effect would this new building have on the mean and standard deviation for 1B1R in Avocado Park?

C. If the Avocado Park Housing Authority issued vouchers to subsidize all 1B1Rs in the neighborhood and they lowered the rent on each unit by exactly $100 per month, what would the new mean and standard deviation be for the cost of renting a 1B1R in Avocado Park.

Answer 1

A. An unusual apartment would be one that has a rental cost that is more than two standard deviations away from the mean.

Mean - 2 * Standard deviation = $1050 - 2*$125 = $1050 - $250 = $800

Hence, an apartment costing less than $900 per month would not be considered unusual, but rental below $800 would be considered unusual.

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B. Since the price that Hadey is offering is less than the mean, addition of this unit will lower the mean of 1B1R in Avocado Park. Also, this value is only $50 away from the earlier mean, and will be even lesser away from the new mean, the standard deviation of the cost will also decrease.

Hence, the mean and standard deviation for 1B1R in Avocado Park will decrease.

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C. If the rent of all houses on each unit are lowered by $100, then the overall mean will be also be lowered by $100. Since the differences between the values and the mean will still remain the same, and the number of houses are still the same, there will be no impact on the standard deviation and it will remain the same.

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Kindly comment in case any additional clarifications are required. Thanks.