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his Question: 1 pt 7 of 12 (6 complete) ores of an lQ test have a bell-shaped di

ID: 3321814 • Letter: H

Question

his Question: 1 pt 7 of 12 (6 complete) ores of an lQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the (a) What percentage of people has an IQ score between 67 and 133 (b) What percentage of people has an IQ score less than 78 or greater than 122 (c) What percentage of people has an IQ score greater than 1337 following (a) 96 (Type an integer or a decimal ) (b) % (Type an integer or a decimal ) (01-1% (Type an integer or a decimal ) Enter your answer in each of the answer boxes

Explanation / Answer

mean = 100
std. dev. (sigma) = 11

a)
67 = mean - 3*sigma
133 = mean + 3*sigma

As per empirical rule 99.7% of population lies within 3 sigma levels of the mean.

Hence 99.7% people have IQ between 67 and 133

b)
78 = mean - 2*sigma
12 = mean + 2*sigma

As per empirical rule 95% of population lies within 2 sigma levels of the mean.

Hence 1 - 95% = 5% people has IQ less than 78 or greater than 122.

c)
133 = mean + 3*sigma

As per empirical rule 99.7% of population lies within 3 sigma levels of the mean.

This means area covered by the curve for x>133 is (1- 0.997)/2 = 0.0015

Hence 0.15% people have IQ greater than 133