# Download Let X be a normal random variable with mean 410

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Birthday problem wikipedia, lookup

Inverse problem wikipedia, lookup

Knapsack problem wikipedia, lookup

Transcript
```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
```