The brain volumes (cm cubed) of 20 brains have a mean of 1116.2 cm cubed and a standard deviation of 127.7 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 1411.6 cm cubed be significantly high?

Yes

Explanation:

Range rule of thumb predicts the Range to be  a multiple of 4 of the standard deviation or to be four times  the standard deviation. Making the usual values equal to 2 standard deviations distanct of the mean of the data distribution.

In a given distribution with mean and standard deviation that is obtained, the usual values in mean (as seen in the attached image).

2*standard deviation and mean + 2*standard deviation.

If the data point is not up to the mean

- 2* standard deviation is taken to be significantly low.

If the data point is more than the mean

+ 2*standard deviation is taken to be significantly high.

Let's take the xbar to be the mean and s as standard deviaiton

Given,

mean, xbar = 1116.2

standard deviation, s =127.7

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

Lower boundary

      = xbar - 2s

       = 1116.2 - 2(127.7)

       = 860.8

Upper boundary

      = xbar + 2s

       = 1116.2 + 2(127.7)

       = 1371.6

We should note that 1411.6 is not between 860.8 and 1371.6, which connotes that 1411.6cm^3 is unusually high.

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