Question 1162675
there is an online calculator that will do this for you easily.
that calculator can be found at <a href = "" target = "_blank"></a>


here are the results from using that calculator.


question A probability of the sale price being less than 278,000 = .0668072.


<img src = "http://theo.x10hosting.com/2020/072503.jpg" >


question A probability of the sale price being greater than 333,000 = .00003167124.


<img src = "http://theo.x10hosting.com/2020/072504.jpg" >


question B probability of the sale price being less than 278,000 = .1419884.


<img src = "http://theo.x10hosting.com/2020/072505.jpg" >


question B probability of the sale price being greater than 333,000 = .002137367.


<img src = "http://theo.x10hosting.com/2020/072506.jpg" >


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 <a href = "https://www.omnicalculator.com/statistics/normal-distribution" target = "_blank">https://www.omnicalculator.com/statistics/normal-distribution</a>


the z-score table can be found at <a href = "https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf" target = "_blank">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>