Question

The value of homes sold in Hampton VA are normally distributed with a mean of $200,000

and a standard deviation of $10,000. If 1216 houses were sold in 2012, how many houses would

have a value greater than one standard deviation above the mean?

Answer 1

`X \sim N(200000,100000)`

Where
`\mu=200000` and
`\sigma=10000`

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

`Number = 1216*0.16 = 194.56`

And the answer woud be between 194 and 195 houses

Explanation:

Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:

`X \sim N(200000,100000)`

Where
`\mu=200000` and
`\sigma=10000`

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

`Number = 1216*0.16 = 194.56`

And the answer woud be between 194 and 195 houses