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Normal Modelling of IQ Test Scores

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I find this question really difficult to answer and I need help formulating a response.

Some IQ tests are standardized to a normal model with a mean of 100 and a standard deviation of 16.

a. Draw a model for these IQ scores, clearly label it , showing what the 65-95-99.7 rule predicts about the score.

b. In what interval would you expect the central 95% of IQ scores be found

c. About what percent of people should have IQ scores above 116?

d. About what percent of people should have IQ scores between 68 and 84?

e. About what percent of people should have IQ scores abouve 132?

Thank you.

https://brainmass.com/statistics/normal-distribution/normal-modelling-iq-test-scores-478415

SOLUTION This solution is FREE courtesy of BrainMass!

Some IQ tests are standardized to a normal model with a mean of 100 and a standard deviation of 16.

a. Draw a model for these IQ scores, clearly label it , showing what the 68-95-99.7 rule predicts about the score.

68% of data lies within one standard deviation from mean:
100-16 = 84, 100+16 = 116

Thus 68% of IQ score lies within 84 and 116.

95% of data lies within two standard deviations from mean:
100-2*16 = 68, 100+2*16 = 132

Thus 95% of IQ score lies within 68 and 132.

99.7% of data lies within three standard deviations from mean:
100-3*16 = 52, 100+3*16 = 148

Thus 99.7% of IQ score lies within 52 and 148.

b. In what interval would you expect the central 95% of IQ scores be found

95% of data lies within two standard deviations from mean:
100-2*16 = 68, 100+2*16 = 132

Thus 95% of IQ score lies within 68 and 132.

c. About what percent of people should have IQ scores above 116?

Percent of people should have IQ scores above 116 = 50% - 34% = 16%

d. about what percent of people should have IQ scores between 68 and 84?

Percent of people should have IQ scores between 68 and 84 = 47.5 - 34 = 13.5%

e. about what percent of people should have IQ scores above 132?

percent of people should have IQ scores above 132 = (1/2)(100% -95%) = 2.5%