I don't know what your "rule of thumb" is, but:
a. 95% = mean ± 1.96 SD
b. Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
c. If the probability is < .0250 in the smaller portion, the physician might be concerned.
A physician routinely makes physical examinations of children. She is concerned that a three-year-old girl has a height of only 87.8 cm. Heights of three-year-old girls have a mean of 97.5 cm and a standard deviation of 6.9 cm (based on data from the National Health and Nutrition Examination Survey).
a. Use the range rule of thumb to find the maximum and minimum usual heights of three-year-old girls.
b. Based on the result, is the height of 87.8 cm unusual?
c. Should the physician be concerned?
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