Question 658524: Cumulative Standard Normal Score Distribution Charts. I sure hope one of you tutors have some earthly idea's on this. If you can explain in simple language how to find and work a z-score. Example: a question from my work sheet.
Find the z-score for the standard normal distribution where: P(z<+a)=0.9625.
or the other one is: If the random variable z is a Standard Normal Score, what is P(-2.00 <_ z <_ +2.00)? How did you find this probability?
We are not suppoose to use any calulators or anything but the Cumulative Standard Normal Table Charts.
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,Re TY, good news is that You will not be expected to do this "long-hand"
that's why there are charts, Excel functions, calculators like the TI83, etc
to find either the z-value given the P-value or the P-value given the z-value
for ex: using Excel function: NORMSINV(.9625) = 1.7805
and P(-2.00 <_ z <_ +2.00)= NORMSDIST(2)-NORMSDIST(-2) = .9544
Important to Understand z -values as they relate to the Standard Normal curve:
Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
Note: z = 0 , 50% of the area under the curve is to the left and 50% to the right
This particular 'chart' below shows the amount of area under the Normal distribution curve between z = 0 and the z given
(half the total area to the left of the z-value)
that is to say one would add .50 to each entry for total area under the curve to the left of the z value.
Highlighted + .50 is .9625 and P(z<+a)=0.9625, a = 1.78 (the 8 coming from the .08 column)
As to P(-2.00 <_ z <_ +2.00) = .4772 + .4772 = .9544
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389
1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616  0.4633
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767
2.0  0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
|
|
|
