Answer:
Not significantly high
Explanation:
Solution:-
- A sample of n = 20 brains was investigated for the total occupied volume in ( cm^3 ).
- The random variable ( X ) would be assigned to the occupied volume of a brain.
- The random variable ( X ) is said to be normally distributed with the following parameters:
X ~ Norm ( μ , σ^2 )
- The normal distribution parameters mean ( μ ) and standard deviation ( σ ) are given:
X ~ Norm ( 1169.2 , 122.4^2 )
- The rule of thumb for outliers ( significantly high or low ) value with respect to the normal distribution is defined as:
Significantly High: X > μ + 3*σ
Significantly Low : X < μ - 3*σ
- These limits corresponds to the property of normal distribution that 99.7% of the data points lie within 3 standard deviations about the mean.
- Any value that lies outside this bound have statistical probability of 0.003 or ( 1.3 % ) significance to the data. Very low significance or value that is considered to be an outlier ( odd value ).
- The bound for the given data can be determined:
[ μ - 3*σ < X < μ + 3*σ ]
[ 1169.2 - 3*122.4 < X < 1169.2 + 3*122.4 ]
[ 802 < X < 1536.4 ] cm^3
- The value of X = 1384.0 cm^3 lies well within the outlier bound, and in fact it lies within 2 standard deviations. This can be determined by computing the standardized Z-score value:
Z = ( X - μ ) / σ
Z = ( 1384.0 - 1169.2 ) / ( 122.4 )
Z = 1.755 .. (1.75 standard deviation)
- Therefore, for such data a brain volume of 1384.0 cm^3 would NOT be considered significantly high.