Download Let X be a normal random variable with mean 410

Let X be a normal random variable with mean 410 and standard deviation 40.
Find Pr[360<X<440 ]. Give answer as a decimal number correct to two decimal places.
Solution:
We have to X-scores in our question that we have to convert to Z-scores. We do this by
using the Z-Conversion formula for each one:
Z
X 

We are given   410
and
  40
Converting 360 to a Z we get:
360  410
 1.25
40
Converting 440 to a Z we get:
440  410
 0.75
40
So, our problem now becomes Pr[1.25  Z  0.75]
We can solve this problem by using the Normal Approximation Table (Appendix B in the
text).
First look up Z = 0.75.
Now, look up Z = -1.25
It says .7734
It says .1056
So, our answer is .7734 — .1056 = .6678