Solusyon - Pangkabuuang probabilidad sa standard normal na distribusyon

Pangkabuuang probabilidad

50 %

50%

Tingnan ang mga hakbang

Hakbang-sa-hakbang na paliwanag

1. Alamin ang pangkabuuang probabilidad ng mga halaga ng z-score hanggang sa $100$

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 $100$ ay $1$ .
$p (a < 100) = 1$
Ang pangkabuuang probabilidad na $a < 100$ ay $100 %$

2. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores na mas mataas kaysa sa $100$

Ang pambuong probabilidad ng mga halaga na mas malaki kaysa sa $100$ ay $0$ .

$p (a > 100) = 0$
Ang pambuong probabilidad ng $a > 100$ ay $0 %$

3. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores hanggang sa $0$

Gamitin ang positibo o negatibong z-table upang mahanap ang katumbas na halaga para sa $0$ . Ang halagang ito ay ang cumulative na probablidad ng area sa kaliwa ng $0$ .

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-score na $0$ ay tumutugma sa area ng $0.50000$
$p (a < 0) = 0.50000$
Ang cumulative na probablidad na $a < 0$ ay $50 %$

4. Kalkulahin ang cumulative na probablidad ng mga halaga na mas mataas kaysa sa 100 at mas mababa kaysa sa 0

Idagdag ang cumulative probability ng lugar sa kanan ng mas mataas na z-score (lahat sa kanan ng $100$ ) sa cumulative probability ng lugar sa kaliwa ng mas mababang z-score (lahat sa kaliwa ng $0):$ $0 + 0.5 = 0.5$
$p (0 > a > 100) = 0.5$
Ang cumulative probability na $0 > a > 100$ ay $50 %$

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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 100

2. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores na mas mataas kaysa sa 100

3. Hanapin ang cumulative na probablidad ng mga halaga ng z-scores hanggang sa 0