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 g
iven 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?
1 answer:
Answer:
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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