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​?

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.