Question

The brain volumes

​(cm cubedcm3​)

of 20 brains have a mean of

1155.11155.1

cm cubedcm3

and a standard deviation of

121.5121.5

cm cubedcm3.

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

1378.11378.1

cm cubedcm3

be significantly​ high?

Significa

Answer 1

Let X be the brain volume ​() of any given brain. We have been given that the sample mean of 20 brains is and sample standard deviation is

The rule of thumb is to classify the values which are 3 standard deviations below the mean as significantly low and 3 standard deviations above the mean as significantly high.

The value which is 3 standard deviations below the mean is

The value which is 3 standard deviations above the mean is

ans:  the limits separating values that are significantly low or significantly high is [790.6,1519.6]

The value 1378.1 lies within the interval [790.6,1519.6] .

ans: Since the value 1378.1 is lower than the high limit 1519.6,  we can say that such a brain volume is not significantly high.

Alternatively, we can see if the z score of 1378.1 is higher than 3 or lower than -3.

The z score of a brain volume of 1378.1 is

Since the z score of 1378.1 is lower than 3, we can say that such a brain volume is not significantly high.