q 11 A physician routinely makes physical examinations of children and is concer

Question

q 11

A physician routinely makes physical examinations of children and is concerned that a three-year-old has a height of only 81 centimeters. Heights of 3-year-old girls have a mean of 97.5 cm and a standard deviation of 6.9 cm. Use the Range Rule of Thumb to find the maximum and minimum usual heights of three-year girls. Based on the result, is the height of HI cm unusual for a three-year-old girl? Clearly show and explain the justification for your choice including your calculations. 1Q scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. According to the Empirical Rule, what percentage of IQ scores are between 70 and 130? Clearly show and explain the justification for your choice including your calculations. According to Chebyshev's Theorem for any data set, what part of a data set will lie within three stan deviations of the mean?

Explanation / Answer

#11

a) According to range rule of thumb, any height between - 2 and + 2 is considered as usual.

- 2 = 97.5 - 2(6.9) = 83.7 cm

+ 2 = 97.5 + 2(6.9) = 111.3 cm

Usual heights are between 83.7 cm and 111.3 cm.

b) Since 81 is below 83.7, its unusual.

c) Any height below 83.7 cm and above 111.3 cm is considered as unusual.

#12

a) 70 and 130 are 2 standard deviations away from mean. According to empirical rule, 95% IQ scores are between 70 and 130.

b)

100-2(15) = 70

100+2(15)=130

#13 According to Chebyshev's theorem,

1-1/k2 = 1 - 1/32 = 0.8889 = 88.89% of the data set lies within 3 standard deviations of the mean.

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