According to the figure, which one is false about a normally-distributed random variable with mean M and standard deviation S? Probability of Cases in portions of the curve Standard Deviations From The Mean Cumulative The Normal Distribution A 1960 95% of values 99% of values -83413 Values -0.0013 -2.58 -30 + 0.1% + -00214 -20 2.3% + +0.1359 -10 15.9% 50% +10 84.1% -0.1359 +20 97.7% → 2560 -00214 +30 99.9% -0.0013 O The probability of an observation at least one standard deviation more than M is almost 15.9%. The probability of an outcome at least three standard deviations away from M is less than 1%. Almost 95% of all observations are in the interval [M- 2.58 S, M + 2.58 S]. Almost 2.3\% of observations are less than M - 2S.
According to the figure, which one is false about a normally-distributed random variable with mean M and standard deviation S? Probability of Cases in portions of the curve Standard Deviations From The Mean Cumulative The Normal Distribution A 1960 95% of values 99% of values -83413 Values -0.0013 -2.58 -30 + 0.1% + -00214 -20 2.3% + +0.1359 -10 15.9% 50% +10 84.1% -0.1359 +20 97.7% → 2560 -00214 +30 99.9% -0.0013 O The probability of an observation at least one standard deviation more than M is almost 15.9%. The probability of an outcome at least three standard deviations away from M is less than 1%. Almost 95% of all observations are in the interval [M- 2.58 S, M + 2.58 S]. Almost 2.3\% of observations are less than M - 2S.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![According to the figure, which one is false about a normally-distributed random variable with mean M
and standard deviation S?
Probability of Cases
in portions of the curve
Standard Deviations
From The Mean
Cumulative %
The
Normal
Distribution
4
-40
Values
-0.0013
-2.580
-30
0.1%
-1.960
-0.0214
-20
2.3%
0.1359
-10
15.9%
95% of values
99% of values
0.3413
0
50%
-0.3413
+10
84.1%
0.1359
1.960
+20
97.7%
2.580
→ 0.0214
1
+30
99.9%
-0.0013
+40
The probability of an observation at least one standard deviation more than M is almost 15.9%.
The probability of an outcome at least three standard deviations away from M is less than 1%.
Almost 95% of all observations are in the interval [M- 2.58 S, M + 2.58 S].
Almost 2.3\% of observations are less than M - 2S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94e6d1f-417b-4288-9be7-d0bb82266d6b%2Fb9e8d391-c0fe-4174-9d42-3c00d4e0c59d%2Fhje3pqx_processed.png&w=3840&q=75)
Transcribed Image Text:According to the figure, which one is false about a normally-distributed random variable with mean M
and standard deviation S?
Probability of Cases
in portions of the curve
Standard Deviations
From The Mean
Cumulative %
The
Normal
Distribution
4
-40
Values
-0.0013
-2.580
-30
0.1%
-1.960
-0.0214
-20
2.3%
0.1359
-10
15.9%
95% of values
99% of values
0.3413
0
50%
-0.3413
+10
84.1%
0.1359
1.960
+20
97.7%
2.580
→ 0.0214
1
+30
99.9%
-0.0013
+40
The probability of an observation at least one standard deviation more than M is almost 15.9%.
The probability of an outcome at least three standard deviations away from M is less than 1%.
Almost 95% of all observations are in the interval [M- 2.58 S, M + 2.58 S].
Almost 2.3\% of observations are less than M - 2S.
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