Scores on the LSAT are approximately normally distributed. In fact, published reports indicate that approximately 40 percent of all test takers score at or between 145 and 155, and about 70 percent score at or between 140 and 160. The full range of scores is 60 pts (120–180). Using your knowledge of normal distributions, estimate the mean, median, and the standard deviation of the LSAT.
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Percentage of scores falling above a z of 1.44.
To estimate the mean, median, and standard deviation of the LSAT scores, we can use the information given about the percentage of test-takers within specific score ranges.
1. Estimating the Mean:
Since the LSAT scores are approximately normally distributed, the mean will be at the center of the distribution. Since the full range of scores is 60 points (from 120 to 180), and approximately 40% of test-takers score between 145 and 155, we can assume that this range corresponds to approximately 1 standard deviation (since about 68% of a normal distribution falls within 1 standard deviation of the mean). Therefore, we can estimate that the mean of the LSAT scores is around (145 + 155) / 2 = 150.
2. Estimating the Standard Deviation:
Since approximately 70% of test-takers score between 140 and 160, which corresponds to about 2 standard deviations (since about 95% of a normal distribution falls within 2 standard deviations of the mean), we can estimate that the standard deviation of the LSAT scores is (160 - 140) / 2 = 10.
3. Estimating the Median:
The median represents the score that divides the distribution into two equal halves, and for a normally distributed variable, the mean and median are the same. Therefore, we can estimate that the median of the LSAT scores is also around 150.
Please note that these estimates are based on the information provided about the percentage of test-takers within specific score ranges.