SOLUTION: I need HELP badly. The diameters of grapefruits in Jones Orchard are NORMALLY distributed with a Mean of 6.70 inches and a Standard deviation of 0.60 inches. How is this do

 

Hi,

95.25% of the granpefruits in Jones Orchard have diameters less than 7.4 inches

22.66% of the grapefruits in Jones Orchard are larger than 7.15

you didn't say WHAT You need help with: NORMALLY distributed...μ =6.7 ,  σ =.6 

P(x < 7.4) = P( z ≤ (7.4-6.7)/.6) 

           = P(z ≤  1 .667) Or P(z≤ 1.67) = .9525 (below table)  Or 95.25%

P(x < 7.15) = P( z ≤ (7.15-6.7)/.6) etc...

P(x > 7.15) = 1 - P( z ≤ (7.15-6.7)/.6) = 1 - P(z = .75) 

from chart:  1 - .7734 = .2266  0r  22.66%

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.



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		0.2764	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