5 The average price for an acre of land in Wyoming is N2500

5) The average price for an acre of land in Wyoming is N(2500, 700²) in dollars.   Jaime surveys 49 plots of land in the Albany county to make sure that they are priced the same as the rest of Wyoming. Assuming that the Albany county is actually priced similar to the rest of Wyoming, find the probability that the first plot of land that Jaime surveyed had a price higher than $3,000.

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    3000      
u = mean =    2500      
          
s = standard deviation =    83.67795409      
          
Thus,          
          
z = (x - u) / s =    5.975289495      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   5.975289495   ) =    0.00000000114841 [ANSWER]