Question 1186247
you can find the area to the left of -2.81 and the area to the left of -1.24.
you would then subtract the smaller area from the larger area.
the remainder is the area between those two z-scores.


alternatively, you can find the area in between directly, depending on the capabilities of the normal distribution calculator that you use.


you can also do it using a z-score table that tells you the area to the left of the z-score.


using the z-score table at <a href = "https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf" target = "_blank">https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf</a>, i get the following.


area to the left of -2.81 = .00248.
area to the left of -1.24 = .10749.


the units and tens digit of the z-score is on the left in the first column.
the hundreds digit is on that row with the first column to the right = .00, then up each digit until .09.


for example, -1.24 shows -1.2 on the first column and then .04 on the fifth column of that row.
together they make  -1.24 because -1.2 + .04 = -1.24.


if you look at the column heading on the top of each page, you'll see that's what it shows in the firth column, i.e. .04


here's a display, broken down to show you the heading of the columns and the particular rows of interest.


<img src = "http://theo.x10hosting.com/2021/101701a.jpg" >


<img src = "http://theo.x10hosting.com/2021/101701b.jpg" >


<img src = "http://theo.x10hosting.com/2021/101701c.jpg" >


here's what the table looked like before i cut it up.


<img src = "http://theo.x10hosting.com/2021/101701d.jpg" >



subtract smaller area from larger area to get area in between = .10501.


my ti-84 plus tells me that the area in between is .1050106258 = .10501 rounded to 5 decimal digits.


using the calculator at <a href = "https://www.statskingdom.com/normal.html" target = "_blank">https://www.statskingdom.com/normal.html</a>, i get:


area in between = .10501 when rounded to 5 decimal laces.


here's a display from that calculator.


<img src = "http://theo.x10hosting.com/2021/101702.jpg" >


using the same calculator, and only looking for the area to the left of the z-score, i get:


area to the left of -1.24 = .10748800
area to the left of -2.81 = .00247707


here are the displays from that calculator.


<img src = "http://theo.x10hosting.com/2021/101703.jpg" >


<img src = "http://theo.x10hosting.com/2021/101704.jpg" >


you're looking for the second entry under the calculate button.


area in between is smaller area subtracted from larger area = .10105093 = .10501 when rounded to 5 decimal digits.


here are the displays from that calculator.