Question 1162675: 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 $400,000, the company believes that it will be able to get an average sale price of $293,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $10,000. [You may find it useful to reference the z table.]
a. What is the probability that the condominium will sell at a price (i) Below $278,000?, (ii) Above $333,000? (Round "z" value to 2 decimal places and 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 $293,000, but with a higher standard deviation of $14,000. What is the probability that this condo will sell at a price (i) Below $278,000?, (ii) Above $333,000? (Round your answers to 4 decimal places.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there is an online calculator that will do this for you easily.
that calculator can be found at
here are the results from using that calculator.
question A probability of the sale price being less than 278,000 = .0668072.
question A probability of the sale price being greater than 333,000 = .00003167124.
question B probability of the sale price being less than 278,000 = .1419884.
question B probability of the sale price being greater than 333,000 = .002137367.
using the z-scores and the table sis more cumbersome.
i'll do question a for you to show you how it's done.
mean = 293.000
standard deviation = 10,000
z-score = (x - m) / sd
z-score for below 278,000 is z = (278,000 - 293,000) / 10,000.
solve for z-score to get z = -1.50.
look in the tables to find the probability of getting a z-score less than that.
that would be the area to the left of the z-score.
the area to the left of a z-score of -1.50 is equal to .06681.
.06681 is the probability that the price will be less than 278,000.
z-score for above 333,000 is z = (333,000 - 293,000) / 10,000.
solve for z-score to get z = 4.
look in the tables to find the probability of getting a z-score less than that.
that would be the area to the left of the z-score.
the area to the left of a z-score of 4 is off the chart.
the closest value shown is a z-score of 3.99 which has an area to the left of it of .99997
the area to the right of that z-score is equal to 1 - .99997 = .00003.
.00003 is the probability that the price will be above 330,000, as close as i can get it, using the table.
compare the calculator results to the table results.
calculator says the probability that the price is less than 278,000 is equal to .0668072.
table says the probability that the price is less than 278,000 is equal to .06681
calculator says the probability that the price is greater than 333,000 is .00003167124.
table says the probability that the price is greater than 333,000 is .00003.
obviously, the calculator give you a much more detailed answer that is accurate to more decimal digits.
i used the TI-84 Plus to confirm the results.
the TI-84 Plus gave me the following results.
for part a (standard deviation = 10,000):
p(less than 278,000) = .0668072287
p(greater than 333,000) = .00003168603459
for part b (standard deviation = 14,000):
p(less than 278,000) = .1419884174
p(greater than 333,000) = .0021374316
if you round all answers to 4 decimal places, then you get the following.
question A p(less than 278,000)
online calculator = .0668
z-table = .0668
ti-84 = .0668
question A p(greater than 333,000)
online calculator = .0000
z-table = .0000
ti-84 = .0000
question B (less than 278,000)
online calculator = .1420
ti-84 = .1420
question B (greater than 333,000)
online calculator = .0021
ti-84 = .0021
i didn't do the z-table for question B.
you are free to do it yourself, using the method i shoed you for question A.
keep in mind that standard deviation for question B is 14,000 while standard deviation for question A was 10,000
the online calculator can be found at https://www.omnicalculator.com/statistics/normal-distribution
the z-score table can be found at https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf
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