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The rent for a one-bedroom apartment in Southern California follows the normal d

ID: 3131497 • Letter: T

Question

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,350 per month and a standard deviation of $260 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed.

    

What is the probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month?

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,350 per month and a standard deviation of $260 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    2260      
u = mean =    2350      
n = sample size =    65      
s = standard deviation =    260      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.790781528      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -2.790781528   ) =    0.997370952 [ANSWER]