Question

The average one-bedroom apartment rents for $2,000 a month in Washington, D.C., with a standard deviation of $400. A real estate agent is looking to find a one-bedroom apartment for a client that is in the top 15% of all rentals in the city. How much should a client expect to pay for a one-bedroom apartment in the top 15% of rentals if the agent only surveys 50apartments in the city? Use the z-table below:
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.7 0.758 0.761 0.764 0.767 0.770 0.773 0.776 0.779 0.782 0.785
0.8 0.788 0.791 0.794 0.797 0.800 0.802 0.805 0.808 0.811 0.813
0.9 0.816 0.819 0.821 0.824 0.826 0.829 0.831 0.834 0.836 0.839
1.0 0.841 0.844 0.846 0.848 0.851 0.853 0.855 0.858 0.860 0.862
1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.883
1.2 0.885 0.887 0.889 0.891 0.893 0.894 0.896 0.898 0.900 0.901
1.3 0.903 0.905 0.907 0.908 0.910 0.911 0.913 0.915 0.916 0.918
Round the z-score, σx¯ and x¯ to two decimal places.

Answer 1

Answer:

$2,058

Step-by-step explanation:

The calculation of the amount expected to pay is shown below:-

Z value for top 15% area = 1.04

(with the help of using z-table)

now,

we will  

Find the corresponding value to 1 - 0.15

= 0.85

Now

$X = \mu + Z\times \frac{\sigma}{\sqrt{n} }$

$X = \ 2,000+ 1.04 \times \frac{\ 400}{\sqrt{50}}$

$X = \ 2,000+ 1.04 \times 56.56854249$

X = 2058.831284

or

= $2059 approx

Hence, the amount expected to pay for a one-bedroom apartment is $2,058

Therefore we applied the above formula