Question Help Scores of an lQ test have a bell-shaped distribution with a mean o

Question

Question Help Scores of an lQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. Use the empirical rule to determine the following (a) What percentage of people has an IQ score between 55 and 145? (b) What percentage of people has an IQ score less than 85 or greater than 115? (c) What percentage of people has an IQ score greater than 130? (a) % (Type an integer or a decimal.) (b) | | % (Type an integer or a decimal.) (c) % (Type an integer or a decimal ) Enter vour answer in each of the answer boxes

Explanation / Answer

apply 68-95-99.7 rule here

a) 55 and 145 are 3 sd away from mean as 55 = 100 -3*15 and 145 = 100 +3*15
hence 99.7 %
b) P(X< 85 or X > 115)
= 1 - P(85 < X< 115)
= 1 - 0.68 = 0.32
= 32 %

c) P(X > 130)
2 sd away = 0.5 - 0.95/2 = 0.025
= 2.5 %

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