1. \( \mu=23 ; \sigma=7 \); two standard deviations above the mean

Two standard deviations above the mean can be calculated by adding \(2 \times \sigma\) to the mean. So, in this case, you would compute \(23 + 2 \times 7\), which equals \(23 + 14 = 37\). This means that any value above 37 would be considered more than two standard deviations above the mean, putting it quite far in the higher range of your data. Understanding the implications of this can be very useful. For instance, in a classroom with an average score (mean) of 23 and a standard deviation of 7, a score of 37 or above indicates exceptional performance, often standing out among peers and reflecting significant achievement in that context.