If Soni got an intelligence score of 115, then what percentage of the population (% as given in the graph) will have intelligence scores higher than the score obtained by Soni? (rounded off to 2 decimal places)
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In a normal distribution, you can calculate the percentage of values above or below a given score by summing up the relevant areas under the curve. These areas correspond to the probability or percentage of the population in that range.
The given graph represents a normal distribution with the mean (M) at 100. The standard deviation (SD) is divided into different sections as follows:
- The percentage of the population between different ranges of standard deviations is provided in the graph:
- Between the mean (M) and +1 SD (100 to 105), the percentage is 34.13%.
- Between +1 SD and +2 SD (105 to 115), the percentage is 34.13%.
- Between +2 SD and +3 SD (115 to 120), the percentage is 13.59%.
- Between +3 SD and +4 SD (120 to 130), the percentage is 2.14%.
Soni's score of 115 falls between +1 SD and +2 SD (100 to 120).
- The percentage of the population with intelligence scores higher than 115 includes:
- The percentage from +2 SD to +3 SD (115 to 120), which is 13.59%.
- The percentage from +3 SD to +4 SD (120 to 130), which is 2.14%.
- The percentage from +4 SD to +∞, which is 0.13%.
So, the total percentage higher than 115 is:
\[
13.59\% + 2.14\% + 0.13\% = 15.86\%
\]
Thus, the percentage of the population with intelligence scores higher than Soni’s score is:
\[
\boxed{15.86\%}
\]
