If X is a normal variable with mean 10 and SD 2, then what's the area under the normal curve of X bounded by the interval 7 and 13?
- rotchmLv 74 weeks ago
Many ways to do this. Here are two:
A) Transform your values to z space via z = (x - avg)/sd.
So the 7 becomes ?
And the 13 becomes ?
Now look up in your z table for the area between these two.
This usually requires to look up the individual areas & subtracting them.
What do you get?
B) Note that 7 & 13 are each 1.5 SD from the avg. You can apply
an extension of the 68–95–99.7_rule. Wiki it. You will see that
μ ± 1.5σ is 0.8664.
- llafferLv 74 weeks ago
You can determine this with a z-score table.
The area under a normal curve is 1. So the area of a portion of that will be less than one.
First we need the z-scores of your two endpoints:
n = m + sz
Where n is the data point in question (7 and 13)
m is the mean (10)
s is the standard deviation (2)
z is the z-score (unknown)
7 = 10 + 2z and 13 = 10 + 2z
-3 = 2z and 3 = 2z
-1.5z and 1.5 = z
Using these points in a z-score table gives you the probability of a random data point being less than that point (aka, the area under the curve from -inf to that point).
So if you find the area under z = 1.5 and subtract it from the area under z = -1.5 that overlaps, the result is the area between the points.
P(z = 1.5) - P(z = -1.5)
0.9332 - 0.0668
0.8664 unit² is the answer to your questionSource(s): http://www.z-table.com/