MATH SOLVE

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# Question Help Scores of an IQ test have a bell-shaped distribution with a mean of 100100 and a standard deviation of 1010. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 8080 and 120120? (b) What percentage of people has an IQ score less than 9090 or greater than 110110? (c) What percentage of people has an IQ score greater than 120120?

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Answer:a) 95% percentage of people has an IQ score between 80 and 120.b) 68% percentage of people has an IQ score between 90 and 110. c) 2.5% percentage of people has an IQ score greater than 120. Step-by-step explanation:The empirical formula states that:The empirical rule is known as the three-sigma rule or 68-95-99.7 rule.It is a rule which states that for a normal distribution, almost all data falls within three standard deviations of the mean. 68% of data falls within the first standard deviation that is [tex]\mu \pm \sigma[/tex] 95% of data falls within the second standard deviation that is [tex]\mu \pm 2\sigma[/tex] 99.7% of data falls within the third standard deviation that is [tex]\mu \pm 3\sigma[/tex] a) percentage of people has an IQ score between 80 and 120(80, 120) can be written as:[tex](80, 120) = (100-2(10), 100 + 2(10))\\= (\mu \pm 2\sigma)[/tex]Thus, it is the interval within two standard deviation from the mean.Thus, by empirical formula, 95% percentage of people has an IQ score between 80 and 120.b) percentage of people has an IQ score between 90 and 110(90, 110) can be written as:[tex](90, 110) = (100-1(10), 100 + 1(10))\\= (\mu \pm 1\sigma)[/tex]Thus, it is the interval within one standard deviation from the mean.Thus, by empirical formula, 68% percentage of people has an IQ score between 90 and 110.c) P(score greater than 120)= 1 - percentage of score less than 80 - percentage of score between 80 and 120[tex]= 1 - (95\% + 2.5\%) = 2.5\%[/tex]From empirical formula,2.5% percentage of people has an IQ score greater than 120.