SOLUTION: Find the area under the standard normal curve for the following: (A) P(z > 2.15) (B) P(-1.79 < z < 0) (C) P(-1.71 < z < 1.13)

Algebra ->  Probability-and-statistics -> SOLUTION: Find the area under the standard normal curve for the following: (A) P(z > 2.15) (B) P(-1.79 < z < 0) (C) P(-1.71 < z < 1.13)       Log On


   

Question 660403: Find the area under the standard normal curve for the following:
(A) P(z > 2.15)
(B) P(-1.79 < z < 0)
(C) P(-1.71 < z < 1.13)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

P(z > 2.15) =  1 - P(z ≤ 2.15)= 1 - NORMSDIST(2.15)  =.0158

using below Chart showing the proportion of the area under the Normal distribution curve between z = 0 and the z given 

P(-1.79 < z < 0 ) = .4633

P(-1.71 < z < 1.13 ) = .4564  + .3708

One may use a chart, Excel function NORMSDIST() or TI function normalcdf()



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 proportion of the area under the Normal distribution curve between z = 0 and the z given 



that is to say, one would add .50 to each entry for total area under the curve to the left of a positive z value.



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	0.4625	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	0.4772	0.4778	0.4783	0.4788	0.4793	0.4798	0.4803	0.4808	0.4812	0.4817