( a ) Determine the values of sample average and standard deviation of the data in Problem 19.11.

( b ) Determine the values 1 and 2 standard deviations from the mean. Of the 50 sample points, how many fall within these two ranges?

Question

( a ) Determine the values of sample average and standard deviation of the data in Problem 19.11.

( b ) Determine the values 1 and 2 standard deviations from the mean. Of the 50 sample points, how many fall within these two ranges?

Accepted Answer

[latex](a)[/latex] Convert [latex]P(X) [/latex] data to frequency values to determines.

Sample average: [latex]\overline { X } = 4.6[/latex]

Sample variance: [latex]{ s }^{ 2 }=\frac { 1630 }{ 49 } -\frac { 50 }{ 49 } { \left( 4.6 \right) }^{ 2 }=11.67[/latex]

Std deviations [latex]= { (11.67) }^{ 0.5 } = 3.42[/latex]

[latex](b)[/latex] [latex]\overline { X } \pm 1s[/latex] is [latex]4.6 \pm 3.42 = 1.18 [/latex]and [latex]8.02[/latex]

[latex]25[/latex] values, or [latex]50[/latex]%, are in this range.

[latex]\overline { X } \pm 2s[/latex] is [latex]4.6 \pm 6.84 = –2.24[/latex] and [latex]11.44[/latex]

All [latex]50[/latex] values, or [latex]100[/latex]%, are in this range.

Question : ( a ) Determine the values of sample average and standard de...