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lecture8 - Review Exercise 8.1 Problem Suppose the scores x...

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Review Exercise 8.1 Problem: Suppose the scores x on a col- lege entrance examination are normally dis- tributed with a mean of 550 and a stan- dard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90th percentile of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admis- sion to the university. Solution: Little x and big X . They are used differ- ently. 1
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Two methods—assessing normality Method 1: A natural method you may think of would be using a histogram, or a stem- and-leaf plot, and look at the shape. One should be cautious though it may not be that reliable. Method 2: Find the interquartile range IQR and standard deviation s for the sample, then calculate the ratio IQR/s. If the data (sample) come from a normal population, then IQR/s 1.3. Why? ... Because for a standard normal random variable, the 25th and 75th percentiles are -.67 and .67. So what is the theoretical IQR/ σ ?
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