SOLUTION: For a standard normal distribution, find: P(-2.81 < z < -1.24)

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Question 1186247: For a standard normal distribution, find:
P(-2.81 < z < -1.24)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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 https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf, 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.







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




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 https://www.statskingdom.com/normal.html, i get:

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

here's a display from that calculator.



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.





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.