Question 10Drs. Melnyk and Ahmed conducted a study in which 400 participants completed a 50-point test about their knowledge of statistics. The mean score was 40 with a standard deviation of 5. These results approximated a normal distribution, which means that the probability of a score between 0 and 1 standard deviations was about 34.1%, between 1 and 2 standard deviations was about 13.6%, and above 2 standard deviations was about 2.3%. If Ashley’s score on this test was 50, what percentage of students are below Ashley’s score? 1 point97.7%13.6%99.8%47.7%
Question
Question 10Drs. Melnyk and Ahmed conducted a study in which 400 participants completed a 50-point test about their knowledge of statistics. The mean score was 40 with a standard deviation of 5. These results approximated a normal distribution, which means that the probability of a score between 0 and 1 standard deviations was about 34.1%, between 1 and 2 standard deviations was about 13.6%, and above 2 standard deviations was about 2.3%. If Ashley’s score on this test was 50, what percentage of students are below Ashley’s score? 1 point97.7%13.6%99.8%47.7%
Solution
Ashley's score of 50 is 2 standard deviations above the mean (since the mean is 40 and the standard deviation is 5). According to the normal distribution, about 34.1% of scores are between the mean and 1 standard deviation above it, 13.6% are between 1 and 2 standard deviations above the mean, and 2.3% are more than 2 standard deviations above the mean.
Therefore, to find the percentage of students who scored below Ashley, we add up the percentages of students who scored within these ranges:
34.1% (scores between the mean and 1 standard deviation above) + 34.1% (scores between the mean and 1 standard deviation below, because of the symmetry of the normal distribution) + 13.6% (scores between 1 and 2 standard deviations above the mean) + 13.6% (scores between 1 and 2 standard deviations below the mean) + 2.3% (scores more than 2 standard deviations below the mean) = 97.7%
So, 97.7% of students scored below Ashley.
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