Answer to Question #294962 in Statistics and Probability for dood

Question

The brain volumes (centemeters cubed) of 20 brains have a mean of 1115.9 cm cubed and a standard deviation of 120.9 cm cubed. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such​ data, would a brain volume of 1377.7 cm cubed be significantly​ high?

Answer 1

From the given information,

Mean=1115.9

Standard deviation=120.9

The range rule of thumb shows that the usual values are within 2 standard deviations from the mean.

Therefore,

Lower limit= mean-(2$\times$ standard deviation)=1115.9-(2$\times$120.9)=874.1

Upper limit= mean+(2$\times$ standard deviation)=1115.9+(2$\times$120.9)=1357.7

The limit of values is from 874.1 to 1357.7

A value below 874.1 is considered low and a value above 1357.7 is considered high.

Since the value is 1377.7 is more than the upper limit, it is considered a significantly high value