Scores of an 1Q test have a bell-shaped distribution with a mean of 100 and a st

Question

Scores of an 1Q test have a bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the following (a) What percentage of people has an IQ score between 80 and 120? (b) What percentage of people has an IQ score less than 60 or greater than 140? (c) What percentage of people has an IQ score greater than 140? (a)% (Type an integer or a decimal ) (b)[7%(Type an integer or a decimal ) (c)% (Type an integer or a decimal) Enter your anewer in each of the answer boxes Before you start STATISTICS to search

Explanation / Answer

here mean = 100 and 1 standard deviation = 20

As per the emperical rule 68% lie between the first standard deviation(from 80-120) I.e 34% from 80-100 and 34% from 100-120.

95% lies between 2 standard deviations(60-140). Therefore on the left from 60-100 is 47.5% and on the right from 100-140 is 47.5%.

99.7% lies between 3 standard deviations(40-160). So on the left from 40-100 is 49.85% and on the right from 100-160 is 49.85%

(A) what % lies between 80 and 120---this is 68%

(B) what % is less than 60 or greater than 40. Less than 60 means less than 2 standard deviations which is 50-47.5=2.5%. Greater than 140 means greater than 2 standard deviations which is also 2.5%.

Therefore the required percentage is 2.5+2.5=5%

(C) greater than 140, which is greater than 2 standard deviations which is 2.5%.

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