Sampling Distribution It is reported that the mean monthly rent for a one-bedroo

Question

Sampling Distribution

It is reported that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2631 and the standard deviation is $500. A real estate firm randomly samples 100 apartments to study. Assume the distribution of monthly rents for a one-bedroom apartment without a doorman is relatively normal.

1.) Would it be unusual if the sample mean were greater than $2800? Explain

2.) Would it be unusual for an individual apartment to have a rent more than $2800? Explain.

Explanation / Answer

1.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    2800      
u = mean =    2631      
n = sample size =    100      
s = standard deviation =    500      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    3.38      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   3.38   ) =    0.000362429

As this is a small probability (<0.05), YES, THIS IS UNUSUAL. [ANSWER]

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2.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    2800      
u = mean =    2631      
          
s = standard deviation =    500      
          
Thus,          
          
z = (x - u) / s =    0.338      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.338   ) =    0.367681594

As this is not a small probability ( >0.05), NO, THIS IS NOT AN UNUSUAL EVENT. [ANSWER]

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