Solusi - Probabilitas kumulatif dalam distribusi normal standar

Cumulative probability

9986000 %

9986000%

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Penjelasan langkah demi langkah

1. Find the cumulative probability of the z-scores values up to $3$

Usa la tabla z positiva para encontrar el valor correspondiente a $3$ . Este valor es la probabilidad acumulativa del área a la izquierda de $3$ .

Z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0,0	5	50399	50798	51197	51595	51994	52392	5279	53188	53586
0,1	53983	5438	54776	55172	55567	55962	56356	56749	57142	57535
0,2	57926	58317	58706	59095	59483	59871	60257	60642	61026	61409
0,3	61791	62172	62552	6293	63307	63683	64058	64431	64803	65173
0,4	65542	6591	66276	6664	67003	67364	67724	68082	68439	68793
0,5	69146	69497	69847	70194	7054	70884	71226	71566	71904	7224
0,6	72575	72907	73237	73565	73891	74215	74537	74857	75175	7549
0,7	75804	76115	76424	7673	77035	77337	77637	77935	7823	78524
0,8	78814	79103	79389	79673	79955	80234	80511	80785	81057	81327
0,9	81594	81859	82121	82381	82639	82894	83147	83398	83646	83891
1,0	84134	84375	84614	84849	85083	85314	85543	85769	85993	86214
1,1	86433	8665	86864	87076	87286	87493	87698	879	881	88298
1,2	88493	88686	88877	89065	89251	89435	89617	89796	89973	90147
1,3	9032	9049	90658	90824	90988	91149	91308	91466	91621	91774
1,4	91924	92073	9222	92364	92507	92647	92785	92922	93056	93189
1,5	93319	93448	93574	93699	93822	93943	94062	94179	94295	94408
1,6	9452	9463	94738	94845	9495	95053	95154	95254	95352	95449
1,7	95543	95637	95728	95818	95907	95994	9608	96164	96246	96327
1,8	96407	96485	96562	96638	96712	96784	96856	96926	96995	97062
1,9	97128	97193	97257	9732	97381	97441	975	97558	97615	9767
2,0	97725	97778	97831	97882	97932	97982	9803	98077	98124	98169
2,1	98214	98257	983	98341	98382	98422	98461	985	98537	98574
2,2	9861	98645	98679	98713	98745	98778	98809	9884	9887	98899
2,3	98928	98956	98983	9901	99036	99061	99086	99111	99134	99158
2,4	9918	99202	99224	99245	99266	99286	99305	99324	99343	99361
2,5	99379	99396	99413	9943	99446	99461	99477	99492	99506	9952
2,6	99534	99547	9956	99573	99585	99598	99609	99621	99632	99643
2,7	99653	99664	99674	99683	99693	99702	99711	9972	99728	99736
2,8	99744	99752	9976	99767	99774	99781	99788	99795	99801	99807
2,9	99813	99819	99825	99831	99836	99841	99846	99851	99856	99861
3,0	99865	99869	99874	99878	99882	99886	99889	99893	99896	999
3,1	99903	99906	9991	99913	99916	99918	99921	99924	99926	99929
3,2	99931	99934	99936	99938	9994	99942	99944	99946	99948	9995
3,3	99952	99953	99955	99957	99958	9996	99961	99962	99964	99965
3,4	99966	99968	99969	9997	99971	99972	99973	99974	99975	99976
3,5	99977	99978	99978	99979	9998	99981	99981	99982	99983	99983
3,6	99984	99985	99985	99986	99986	99987	99987	99988	99988	99989
3,7	99989	9999	9999	9999	99991	99991	99992	99992	99992	99992
3,8	99993	99993	99993	99994	99994	99994	99994	99995	99995	99995
3,9	99995	99995	99996	99996	99996	99996	99996	99996	99997	99997

Un puntaje z de $3$ corresponde a un área de $99, 865$
$p (x < 3) = 99, 865$
La probabilidad acumulativa de que $x < 3$ sea $9986500 %$

2. Find the cumulative probability of the z-scores values up to $0$

Use the positive or negative z-table to find the value corresponding to $0$ . This value is the cumulative probability of the area to the left of $0$ .

Z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0,0	5	50399	50798	51197	51595	51994	52392	5279	53188	53586
0,1	53983	5438	54776	55172	55567	55962	56356	56749	57142	57535
0,2	57926	58317	58706	59095	59483	59871	60257	60642	61026	61409
0,3	61791	62172	62552	6293	63307	63683	64058	64431	64803	65173
0,4	65542	6591	66276	6664	67003	67364	67724	68082	68439	68793
0,5	69146	69497	69847	70194	7054	70884	71226	71566	71904	7224
0,6	72575	72907	73237	73565	73891	74215	74537	74857	75175	7549
0,7	75804	76115	76424	7673	77035	77337	77637	77935	7823	78524
0,8	78814	79103	79389	79673	79955	80234	80511	80785	81057	81327
0,9	81594	81859	82121	82381	82639	82894	83147	83398	83646	83891
1,0	84134	84375	84614	84849	85083	85314	85543	85769	85993	86214
1,1	86433	8665	86864	87076	87286	87493	87698	879	881	88298
1,2	88493	88686	88877	89065	89251	89435	89617	89796	89973	90147
1,3	9032	9049	90658	90824	90988	91149	91308	91466	91621	91774
1,4	91924	92073	9222	92364	92507	92647	92785	92922	93056	93189
1,5	93319	93448	93574	93699	93822	93943	94062	94179	94295	94408
1,6	9452	9463	94738	94845	9495	95053	95154	95254	95352	95449
1,7	95543	95637	95728	95818	95907	95994	9608	96164	96246	96327
1,8	96407	96485	96562	96638	96712	96784	96856	96926	96995	97062
1,9	97128	97193	97257	9732	97381	97441	975	97558	97615	9767
2,0	97725	97778	97831	97882	97932	97982	9803	98077	98124	98169
2,1	98214	98257	983	98341	98382	98422	98461	985	98537	98574
2,2	9861	98645	98679	98713	98745	98778	98809	9884	9887	98899
2,3	98928	98956	98983	9901	99036	99061	99086	99111	99134	99158
2,4	9918	99202	99224	99245	99266	99286	99305	99324	99343	99361
2,5	99379	99396	99413	9943	99446	99461	99477	99492	99506	9952
2,6	99534	99547	9956	99573	99585	99598	99609	99621	99632	99643
2,7	99653	99664	99674	99683	99693	99702	99711	9972	99728	99736
2,8	99744	99752	9976	99767	99774	99781	99788	99795	99801	99807
2,9	99813	99819	99825	99831	99836	99841	99846	99851	99856	99861
3,0	99865	99869	99874	99878	99882	99886	99889	99893	99896	999
3,1	99903	99906	9991	99913	99916	99918	99921	99924	99926	99929
3,2	99931	99934	99936	99938	9994	99942	99944	99946	99948	9995
3,3	99952	99953	99955	99957	99958	9996	99961	99962	99964	99965
3,4	99966	99968	99969	9997	99971	99972	99973	99974	99975	99976
3,5	99977	99978	99978	99979	9998	99981	99981	99982	99983	99983
3,6	99984	99985	99985	99986	99986	99987	99987	99988	99988	99989
3,7	99989	9999	9999	9999	99991	99991	99992	99992	99992	99992
3,8	99993	99993	99993	99994	99994	99994	99994	99995	99995	99995
3,9	99995	99995	99996	99996	99996	99996	99996	99996	99997	99997

A z-score of $0$ corresponds to an area of $0, 50000$
$p (x < 0) = 0, 50000$
The cumulative probability that $x < 0$ is $50 %$

3. Calculate the cumulative probability between 3 and 0

To find the cumulative probability of the area between the two z-scores, subtract the smaller cumulative probability (everything to the left of $0$ ) from the larger cumulative probability (everything to the left of $3$ ):

$99, 865 - 5 = 99, 860$
$p (0 < x < 3) = 99, 860$
The cumulative probability that $0 < x < 3$ is $9986000 %$

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Normal and standard normal distributions

Solusi - Probabilitas kumulatif dalam distribusi normal standar

Penjelasan langkah demi langkah

1. Find the cumulative probability of the z-scores values up to 3

2. Find the cumulative probability of the z-scores values up to 0

3. Calculate the cumulative probability between 3 and 0

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Istilah dan topik

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Latihan Terkait Terbaru Dipecahkan

1. Find the cumulative probability of the z-scores values up to $3$

2. Find the cumulative probability of the z-scores values up to $0$