Answer:
Explanation:
The range rule of thumb states that the range of a dataset is approximately four times the standard deviation. Using this rule, we can estimate the range of brain volumes in this dataset:
Range ≈ 4 × standard deviation = 4 × 120.4 cm3 = 481.6 cm3
To identify the limits separating values that are significantly low or significantly high, we can add and subtract half the range to and from the mean:
Lower limit = mean - (range/2) = 1190.7 cm3 - (481.6 cm3 / 2) = 949.9 cm3
Upper limit = mean + (range/2) = 1190.7 cm3 + (481.6 cm3 / 2) = 1431.5 cm3
Therefore, any brain volume below 949.9 cm3 or above 1431.5 cm3 would be considered significantly low or significantly high, respectively.
A brain volume of 1411.5 cm3 is within the range of values that are not considered significantly high or low. Its z-score can be calculated as follows:
z-score = (1411.5 - 1190.7) / 120.4 = 1.84
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.84 or higher is approximately 0.0336. This means that a brain volume of 1411.5 cm3 would be considered uncommon, but not extremely rare.