csat-suneung 2021 Q6

csat-suneung · South-Korea · csat__math-science 3 marks Linear combinations of normal random variables

For a population following the normal distribution $\mathrm { N } \left( 20,5 ^ { 2 } \right)$, a sample of size 16 is randomly extracted and the sample mean is denoted by $\bar { X }$. What is the value of $\mathrm { E } ( \bar { X } ) + \sigma ( \bar { X } )$? [3 points]
(1) $\frac { 83 } { 4 }$
(2) $\frac { 85 } { 4 }$
(3) $\frac { 87 } { 4 }$
(4) $\frac { 89 } { 4 }$
(5) $\frac { 91 } { 4 }$

For a population following the normal distribution $\mathrm { N } \left( 20,5 ^ { 2 } \right)$, a sample of size 16 is randomly extracted and the sample mean is denoted by $\bar { X }$. What is the value of $\mathrm { E } ( \bar { X } ) + \sigma ( \bar { X } )$? [3 points]\\
(1) $\frac { 83 } { 4 }$\\
(2) $\frac { 85 } { 4 }$\\
(3) $\frac { 87 } { 4 }$\\
(4) $\frac { 89 } { 4 }$\\
(5) $\frac { 91 } { 4 }$

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