Solusyon - Pangkabuuang probabilidad sa standard normal na distribusyon

Pangkabuuang probabilidad

97.725 %

97.725%

Tingnan ang mga hakbang

Hakbang-sa-hakbang na paliwanag

1. Alamin ang pangkabuuang probabilidad ng mga halaga ng z-score hanggang sa $10.8$

Higit sa $99.9 %$ ng oras, ang data na may karaniwang normal na distribusyon ay nasa loob ng dagdag o bawas na $3.9$ standard deviations ng mean.

Ang pangkabuuang probabilidad ng mga halaga hanggang sa $10.8$ ay $1$ .
$p (y < 10.8) = 1$
Ang pangkabuuang probabilidad na $y < 10.8$ ay $100 %$

2. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores na mas mataas kaysa sa $10.8$

Ang pambuong probabilidad ng mga halaga na mas malaki kaysa sa $10.8$ ay $0$ .

$p (y > 10.8) = 0$
Ang pambuong probabilidad ng $y > 10.8$ ay $0 %$

3. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores hanggang sa $2$

Gamitin ang positibong z-table upang mahanap ang halagang katugma ng $2$ . Ang halagang ito ang pampamahaging katotohanan ng lugar sa kaliwa ng $2$ .

Z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5	0.50399	0.50798	0.51197	0.51595	0.51994	0.52392	0.5279	0.53188	0.53586
0.1	0.53983	0.5438	0.54776	0.55172	0.55567	0.55962	0.56356	0.56749	0.57142	0.57535
0.2	0.57926	0.58317	0.58706	0.59095	0.59483	0.59871	0.60257	0.60642	0.61026	0.61409
0.3	0.61791	0.62172	0.62552	0.6293	0.63307	0.63683	0.64058	0.64431	0.64803	0.65173
0.4	0.65542	0.6591	0.66276	0.6664	0.67003	0.67364	0.67724	0.68082	0.68439	0.68793
0.5	0.69146	0.69497	0.69847	0.70194	0.7054	0.70884	0.71226	0.71566	0.71904	0.7224
0.6	0.72575	0.72907	0.73237	0.73565	0.73891	0.74215	0.74537	0.74857	0.75175	0.7549
0.7	0.75804	0.76115	0.76424	0.7673	0.77035	0.77337	0.77637	0.77935	0.7823	0.78524
0.8	0.78814	0.79103	0.79389	0.79673	0.79955	0.80234	0.80511	0.80785	0.81057	0.81327
0.9	0.81594	0.81859	0.82121	0.82381	0.82639	0.82894	0.83147	0.83398	0.83646	0.83891
1.0	0.84134	0.84375	0.84614	0.84849	0.85083	0.85314	0.85543	0.85769	0.85993	0.86214
1.1	0.86433	0.8665	0.86864	0.87076	0.87286	0.87493	0.87698	0.879	0.881	0.88298
1.2	0.88493	0.88686	0.88877	0.89065	0.89251	0.89435	0.89617	0.89796	0.89973	0.90147
1.3	0.9032	0.9049	0.90658	0.90824	0.90988	0.91149	0.91308	0.91466	0.91621	0.91774
1.4	0.91924	0.92073	0.9222	0.92364	0.92507	0.92647	0.92785	0.92922	0.93056	0.93189
1.5	0.93319	0.93448	0.93574	0.93699	0.93822	0.93943	0.94062	0.94179	0.94295	0.94408
1.6	0.9452	0.9463	0.94738	0.94845	0.9495	0.95053	0.95154	0.95254	0.95352	0.95449
1.7	0.95543	0.95637	0.95728	0.95818	0.95907	0.95994	0.9608	0.96164	0.96246	0.96327
1.8	0.96407	0.96485	0.96562	0.96638	0.96712	0.96784	0.96856	0.96926	0.96995	0.97062
1.9	0.97128	0.97193	0.97257	0.9732	0.97381	0.97441	0.975	0.97558	0.97615	0.9767
2.0	0.97725	0.97778	0.97831	0.97882	0.97932	0.97982	0.9803	0.98077	0.98124	0.98169
2.1	0.98214	0.98257	0.983	0.98341	0.98382	0.98422	0.98461	0.985	0.98537	0.98574
2.2	0.9861	0.98645	0.98679	0.98713	0.98745	0.98778	0.98809	0.9884	0.9887	0.98899
2.3	0.98928	0.98956	0.98983	0.9901	0.99036	0.99061	0.99086	0.99111	0.99134	0.99158
2.4	0.9918	0.99202	0.99224	0.99245	0.99266	0.99286	0.99305	0.99324	0.99343	0.99361
2.5	0.99379	0.99396	0.99413	0.9943	0.99446	0.99461	0.99477	0.99492	0.99506	0.9952
2.6	0.99534	0.99547	0.9956	0.99573	0.99585	0.99598	0.99609	0.99621	0.99632	0.99643
2.7	0.99653	0.99664	0.99674	0.99683	0.99693	0.99702	0.99711	0.9972	0.99728	0.99736
2.8	0.99744	0.99752	0.9976	0.99767	0.99774	0.99781	0.99788	0.99795	0.99801	0.99807
2.9	0.99813	0.99819	0.99825	0.99831	0.99836	0.99841	0.99846	0.99851	0.99856	0.99861
3.0	0.99865	0.99869	0.99874	0.99878	0.99882	0.99886	0.99889	0.99893	0.99896	0.999
3.1	0.99903	0.99906	0.9991	0.99913	0.99916	0.99918	0.99921	0.99924	0.99926	0.99929
3.2	0.99931	0.99934	0.99936	0.99938	0.9994	0.99942	0.99944	0.99946	0.99948	0.9995
3.3	0.99952	0.99953	0.99955	0.99957	0.99958	0.9996	0.99961	0.99962	0.99964	0.99965
3.4	0.99966	0.99968	0.99969	0.9997	0.99971	0.99972	0.99973	0.99974	0.99975	0.99976
3.5	0.99977	0.99978	0.99978	0.99979	0.9998	0.99981	0.99981	0.99982	0.99983	0.99983
3.6	0.99984	0.99985	0.99985	0.99986	0.99986	0.99987	0.99987	0.99988	0.99988	0.99989
3.7	0.99989	0.9999	0.9999	0.9999	0.99991	0.99991	0.99992	0.99992	0.99992	0.99992
3.8	0.99993	0.99993	0.99993	0.99994	0.99994	0.99994	0.99994	0.99995	0.99995	0.99995
3.9	0.99995	0.99995	0.99996	0.99996	0.99996	0.99996	0.99996	0.99996	0.99997	0.99997

Ang z-iscore na $2$ ay tumutugma sa lugar na $0.97725$
$p (y < 2) = 0.97725$
Ang pampamahaging katotohanan na $y < 2$ ay $97.725 %$

4. Kalkulahin ang cumulative na probablidad ng mga halaga na mas mataas kaysa sa 10.8 at mas mababa kaysa sa 2

Idagdag ang cumulative probability ng lugar sa kanan ng mas mataas na z-score (lahat sa kanan ng $10.8$ ) sa cumulative probability ng lugar sa kaliwa ng mas mababang z-score (lahat sa kaliwa ng $2):$ $0 + 0.97725 = 0.97725$
$p (2 > y > 10.8) = 0.97725$
Ang cumulative probability na $2 > y > 10.8$ ay $97.725 %$

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Solusyon - Pangkabuuang probabilidad sa standard normal na distribusyon

Hakbang-sa-hakbang na paliwanag

1. Alamin ang pangkabuuang probabilidad ng mga halaga ng z-score hanggang sa 10.8

2. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores na mas mataas kaysa sa 10.8

3. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores hanggang sa 2