Answer:
The correct option is C.
Step-by-step explanation:
From the given graph it is clear that the pieces of candy received by Timmy and his five friends are
16, 19, 25, 32, 38, 40
The means of a data set is
[tex]Mean=\frac{\sum{x}}{n}[/tex]
[tex]Mean=\frac{16+19+25+32+38+40}{6}=\frac{170}{6}=28.33[/tex]
The means of the data is 28.33.
[tex]Variance=\frac{\sum{x-Mean}^2}}{n}[/tex]
[tex]\sigma^2=\frac{(16-28.33)^2+(19-28.33)^2+(25-28.33)^2+(32-28.33)^2+(38-28.33)^2+(40-28.33)^2}{6}[/tex]
[tex]\sigma^2=82.22[/tex]
[tex]\sigma=\sqrt{82.22}[/tex]
[tex]\sigma=9.068[/tex]
The standard deviations of the data is 9.068.
We have to find how many standard deviations of the mean do the values fall
The standard deviation for the means are
[tex]\frac{Minimum-mean}{\sigma}=\frac{16-28.33}{9.068}=-1.36[/tex]
-1.36 means approx 2 standard dentition towards the right of mean.
[tex]\frac{Maximum-Mean}{\sigma}=\frac{40-28.33}{9.068}=1.29[/tex]
1.29 means approx 2 standard dentition towards the left of mean.
Therefore the data values fall in 2 standard deviations of the mean.
Option C is correct.
