Q. The median of any normal distribution is the same as its mean. We can use normal calculations to find the quartiles and related descriptive measure for normal distributions.

(a)  What is the area under the standard normal curve to the left of the first quartile? Use this to find the value of the first quartile for a standard normal distribution. Find the third quartile similarly.

(b)  Your work in (a) gives the z-scores for the quartiles of any normal distribution. Scores on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with mean 100 and standard deviation 15. What are the quartiles (1st, 2nd and 3rd quartiles) of WISC scores?

(c)  What is the value of the IQR for the standard normal distribution?

(d)  What percent of the observations in the standard normal distribution are suspected outliers according to the 1.5×IQR criterion? (This percent is the same for any normal distribution.)

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