Given IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15, the proportion of people with IQs above 130 is:

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JeanaShupp JeanaShupp · Answer 1 · 2020-08-25T03:08:04+02:00

Answer: 0.0228 .

Step-by-step explanation:

Given, IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15

Let X denotes the IQ score.

Then, the proportion of people with IQs above 130 is

[tex]P(X>130)=P(\dfrac{X-mean}{ standard\ deviation}>\dfrac{130-100}{15})\\\\= P(Z>2)\ \ \ \[Z=\dfrac{X-mean}{ standard\ deviation}][/tex]

[tex]=1-P(Z<2)\ \ \ [P(Z>z)=1-P(Z<z)]\\\\=1-0.9772\ [\text{By z table}]\\\\=0.0228[/tex]

Hence, the proportion of people with IQs above 130 is 0.0228 .