Question

the average price for an acre of land in texas is n(2800, 7302) in dollars. jaime will survey 64 plots of land in the brazos county to make sure that they are priced the same as the rest of texas. assuming that the brazos county is actually priced similar to the rest of texas, find the probability that the first plot of land that jaime surveys will have a price higher than $3,201.

Answer 1

The probability that the first surveyed plot of land in Brazos County has a price higher than $3,201, assuming it follows the Texas average, is practically 0%.

To find the probability that the first plot of land Jaime surveys in Brazos County has a price higher than $3,201, we can use the normal distribution.

Given that the average price for an acre of land in Texas is normally distributed with a mean
`(\(\mu\))` of $2,800 and a standard deviation
`(\(\sigma\))` of $73.02, we can use the z-score formula to standardize the value of $3,201:

`\[ Z = ((X - \mu))/(\sigma) \]\[ Z = ((3,201 - 2,800))/(73.02) \]\[ Z \approx (401)/(73.02) \]\[ Z \approx 5.49 \]`

Now, we want to find the probability that (Z > 5.49). This is a very high z-score, and the probability associated with it will be extremely close to 1 (or 100%).

`\[ P(Z > 5.49) \approx 0 \]`

Therefore, the probability that the first plot of land Jaime surveys in Brazos County has a price higher than $3,201 is practically 0%.