Question

Let X and Y be normal random variables with means 0 and 2, respectively, and variances 1 and 9, respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 4 decimal places.

1. P(X>0.75)=
2. P(X≤−1.25)=
3. Let Z=(Y−3)/4. Find the mean and the variance of Z.
E[Z]=
var(Z)=
4. P(−1≤Y≤2)=

Answer 1

1 P(X>0.75)= 0.2266

2 P(X≤−1.25)= 0.1056

Let Z=(Y−3)/4. Find the mean and the variance of Z.
3. E[Z]= -0.25

4. var(Z)= 0.5625

5. P(−1≤Y≤2)= 0.3413