SOLUTION: a) How large is the area that lies under the standard normal curve bound between –2.03 and -1.23? b) How large is the area that lies under the standard normal curve to the

Algebra ->  Probability-and-statistics -> SOLUTION: a) How large is the area that lies under the standard normal curve bound between –2.03 and -1.23? b) How large is the area that lies under the standard normal curve to the       Log On


   



Question 848064: a) How large is the area that lies under the standard normal curve bound between –2.03 and -1.23?

b) How large is the area that lies under the standard normal curve to the right of 1.63?

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
a) P[-2.03 Think about what this means. We want all the area left of 1.23, but we want to take away the area left of -2.03.
P[Z<1.23] - P[Z < -2.03]
Notice that the area left of -2.03 is the area right of 2.03, or since the entire area is 1, it's 1 -P[Z<2.03]
So we have:
P[Z<1.23] - (1-P[Z<2.03])
Now we can use the standard normal table. Let's call the standard normal lookup function phi.
phi%281.23%29+-+%281-phi%282.03%29%29
.8907+-+%281-.9788%29+=+highlight%280.8695%29

2. P[Z>1.63]. As I mentioned before, since the entire area under the curve is 1, then 1- P[Z<1.63] is another way to represent this.
Using phi
1+-+phi%281.63%29
1-.9484+=+highlight%28.0516%29