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.

Since the mean, median and mode are the same in a normal distribution, mean and median both probably 150. Since approximately 68% score ±1 SD, I would estimate SD at slightly less than 10.

To estimate the mean, median, and standard deviation of the LSAT scores, we can use the information given about the percentile ranges.

1. Mean:
The mean is the average of all scores. Since the LSAT scores are approximately normally distributed, we can estimate the mean by taking the midpoint of the full range of scores. The full range is 60 points, so the midpoint is (120 + 180) / 2 = 150. Therefore, the estimated mean is 150.

2. Median:
The median is the middle value of a dataset when the values are arranged in ascending or descending order. Since approximately 40 percent of test takers score between 145 and 155, we can estimate the median to be the average of these two values. The median is (145 + 155) / 2 = 150.

3. Standard Deviation:
The standard deviation measures the spread or dispersion of the scores. Given that about 70 percent of test takers score between 140 and 160, we can estimate the standard deviation by calculating the range and dividing it by 4. The range is 160 - 140 = 20, so the estimated standard deviation is 20 / 4 = 5.

Therefore, the estimated mean is 150, the estimated median is 150, and the estimated standard deviation is 5 for the LSAT scores.