Question

G a frequency distribution has a mean of 200 and a standard deviation of 20. the class limits for one class are 220 up to 240. based on the normal distribution, what is the probability that an observation would be in this class?

Answer 1

A suitable probability calculator will show that probability to be .135905122.

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Your class extends from 1 standard deviation above the mean to 2 standard deviations above the mean. The empirical rule puts that probability at ...

... (1/2)(95% - 68%) ≈ 13.5%

The empirical rule tells you 68% of observations lie within 1 standard deviation of the mean, and 95% lie within 2 standard deviations. Then the number that lie between 1 and 2 standard deviations from the mean will be the difference of these values. You want the values in the region above the mean only, so you only want half the difference just described.