In a certain section of Southern California the distribution

In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,200 and a standard deviation of $250. The distribution of the monthly rent does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one-bedroom apartments and finding the mean to be at least $1,950 per month? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    1950      
u = mean =    2200      
n = sample size =    50      
s = standard deviation =    250      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -7.07      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -7.07   ) =    1.0000 [ANSWER, it is very close to 1]