Question

Iq scores within a population are normally distributed with a mean of 100 aand a s.d.10. area enclosed under normal curve for Iq scores above 130 is​

Answer 1

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solution is in attachment

Answer 2

IQ scores within a population are normally distributed with a mean of 100 and standard deviation of 10.

The area under the curve for IQ scores above 130 is calculated as,

$\sf \: μ= 100 \\ \sf \: σ = 10 \: \: \\ \sf \: x=130$

$\sf \: z = \frac{x - μ}{σ} \: \: \: \: \: \: \: \: \\ \\ \sf \: z = \frac{130 - 100}{10}$

$\sf \: z = \frac{30}{10}$

$\sf \: z = 3$

Thus probability for z = 3 is 0.4987 which is 49.87%