Question

A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for $300,000, the company believes that it will be able to get an average sale price of $207,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $13,000.

a. What is the probability that the condominium will sell at a price (i) below $182,000?(ii) above $228,000? (Round final answers to 4 decimal places.)

b. The company is also trying to sell an artist’s condo. Potential buyers will find the unusual features of this condo either pleasing or objectionable. The manager expects the average sale price of this condo to be the same as others at $207,000, but with a higher standard deviation of $17,000. What is the probability that this condo will sell at a price (i) Below $182,000?, (ii) Above $228,000? (Round your answers to 4 decimal places.)

Answer 1

a> Let X be a random variable denoting the price of the condominium.

Here, X N(207,000,13,000^2)

Z= (X-207,000)/13,000 N(0,1)

i ) Pr[ X < 182,000] = Pr[ (X-207,000)/13,000 < (182,000-207,000)/13,000 ]

= Pr[ Z < -1.923076923 ]

=  

= 1 -

= 1 - 0.9725711 [ obtained from statistical tables ( Z table) ]

= 0.0274 ( correct up to 4 decimal places)

ii ) Pr[ X > 228,000 ] = Pr [ (X-207,000)/13,000 > (228,000-207,000)/13,000 ]

= Pr [ Z > 1.615384615 ]

= 1 -

= 1 - 0.9463011  [ obtained from statistical tables ( Z table) ]

= 0.0537 ( correct up to 4 decimal places )

b> Let Y denotes the sell price of the condo.

Y   N(207,000,17,000^2)

Z= (Y-207,000)/17,000 N(0,1)  

i> Pr[ Y < 182,000] = Pr[ (Y-207,000)/17,000 < (182,000-207,000)/17,000 ]

= Pr[ Z < -1.470588235 ]

= 1 -

= 1 - 0.9292191 [ obtained from statistical tables ( Z table) ]

= 0.0708 ( correct up to 4 decimal places )

ii> Pr[ Y > 228,000 ] = Pr [ (Y-207,000)/17,000 > (228,000-207,000)/17,000 ]

   = Pr [ Z > 1.235294118 ]

= 1 -

= 1 - 0.8906514   [ obtained from statistical tables ( Z table) ]

= 0.1093 ( correct up to 4 decimal places )