A particular 1Q test is standardized to a Normal model, with a mean of 100 and a

Question

A particular 1Q test is standardized to a Normal model, with a mean of 100 and a standard deviation of 20. 40 60 80 100 120 140 160 40 60 80 100 120 140 180 b) In what interval would you expect the central 68% of the IQ scores to be found? Using the 68-95-99 7 rule, the central 68% of the IQ scores are between [] and Type integers or decimals. Do not round.) c) About what percent of people should have IQ scores above 160? Using the 68-95-997 Type an integer or a decimal. Do not round.) d) About what percent of people should have IQ scores between 40 and 602 Using the 68-95-99.7 rule, about % of people should have IQ scores between 40 and 60 rule, about l % of people should have IQ scores above 160 Type an integer or a decimal. Do not round.) e) About what percent of people should have IQ scores above 120? Using the 68-95-99.7 rule, about % of people should have IQ scores above 120 (Type an integer or a decimal. Do not round ) Click to select your answer(s)

Explanation / Answer

Data given:

Mean = 100

Standard deviation = 20

(b)

Central 68% lies within 1 SD from the mean, which means between:

(100-20) and (100+20)

which is equal to

80 and 120

(c)

160 is 3 SD above the mean. According to the empirical rule, 0.3% of data lies outside 3 SD away from the mean.

So, % of scores lying above 160 = 0.3/2 = 0.15%

(d)

40 is 3 SD below the mean, and 60 is 2 SD below the mean.

So % of scores lying in this range = (99.7-95)/2 = 2.35%

(e)

120 is 1 SD above the mean, so % of scores above 120 = (100-68)/2 = 16%

Hope this helps !

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