The average monthly rent for apartments in midtown Manhattan

The average monthly rent for apartments in midtown Manhattan are normally distributed with a mean of $4,000. According to a local real estate firm, only 1.7% of the apartments in midtown Manhattan rent for less than $2,834 per month. Based on this information, what is the value of the standard deviation of the monthly rents  for apartments in midtown Manhattan?

Solution

P ( Z < X ) = 0.17
Value of z to the cumulative probability of 0.17 from normal table is -0.954
P( X-u/s.d < X - 4000/ s.d ) = 0.17
That is, ( 2834 - 4000/ s.d ) = -0.9542
--> s.d = ( 2834 - 4000 ) / -0.9542
--> s.d = ( -1166 ) / -0.9542
--> s.d = 1222.0105