Among applicants to one law school, the average LSAT score was about 169 , the SD was about 9, a

step 1 So in this question, we're actually supposed to find out if the Lset curve is following the norm

Among applicants to one law school, the average LSAT score...

Key Concepts

Normal Distribution

The normal distribution is a continuous probability distribution that is symmetric about the mean, forming a bell-shaped curve. It is characterized by two parameters, the mean and the standard deviation, and is fundamental in statistics due to its prevalence in natural phenomena and its role in the Central Limit Theorem. Deviations from normality are often assessed by evaluating how data points spread around the mean and whether the tail behavior conforms to the expected exponential decay.

Empirical Rule

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, around 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. This rule is used as a quick check for normality and to assess whether observed data points, especially those at the extremes, are consistent with a normal distribution.

Extreme Values and Outliers

Extreme values or outliers in a data set are observations that lie far from the mean and are often more than two or three standard deviations away. In a truly normal distribution, large samples are expected to have some observations that are several standard deviations away from the mean. Therefore, if the maximum value observed is only marginally above the mean, it may suggest that the data does not follow a typical normal pattern or that the sample is subject to constraints.

Truncation and Range Limitations

Truncation occurs when a dataset has an imposed limit on possible values, either through selection criteria or physical constraints, resulting in a cut-off in the natural spread of data. In the context of testing scores, if there is a ceiling effect or other limits on scores, the observed distribution may not reflect a normal curve, as the upper tail is artificially shortened. This concept is important when comparing observed ranges to the expected variability under a normal distribution.

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