Final answer:
A Z-score represents the number of standard deviations a data point is from the mean. In this case, a Z-score of 3.5 indicates that the score is 3.5 standard deviations above the mean. Therefore, the correct option is B. 3.5 standard deviations.
Explanation:
A Z-score is a statistical measure that describes a value's relation to the mean of a group of values, and it is measured in terms of standard deviations from the mean. In this context, a Z-score of 3.5 signifies that the data point is 3.5 standard deviations above the mean. The mean is considered the average or central value in a distribution, and standard deviations quantify the amount of variation or dispersion from this mean.
In more concrete terms, a Z-score of 3.5 indicates an extreme position in the distribution, as it is significantly higher than the average. This suggests that the data point is relatively rare and falls well into the tail of the distribution. The formula for calculating a Z-score is (X - μ) / σ, where X is the individual data point, μ is the mean, and σ is the standard deviation. A Z-score above 3 suggests an observation is in the upper tail of the distribution.
Understanding Z-scores is crucial in various fields, such as finance, where it helps identify outliers in stock returns, or in medical research, where it might highlight extreme values in clinical trials. In summary, a Z-score of 3.5 represents a score that is 3.5 standard deviations above the mean, indicating a significant departure from the average.