Question

scores on an iq test are normally distributed. the test is designed so that the mean is 100 and standard deviation is 15. (a) what percentage of the population has an iq above 120?

Answer 1

From the normal distribution it is calculated that 9.18% of people has an iq over 120.

Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued regressors with unknown distributions.

• Some of their significance can be attributed to the central limit theory.
• This claim states that, in some cases, the average of many samples (observations) of a stochastic process with limited mean and variance constitutes itself as a random variable, whose distribution merges to a normal distribution as the number of samples increases.
• Because of this, the distributions of physical values, such as error margins, which are expected to be the sum of many independent events, are frequently near to normal.

We have to find P( X > 120 )

Thus find z score for  x =120

$z=\frac{x-\mu}{\sigma}=\frac{120-100}{15}=\frac{20}{15}=1.33$

Thus we get:

P(X>120) = P(Z>1.33)

P(X>120) = 1 - P(Z<1.33)

P( Z < 2.67) = 0.9082

Thus

P(X>140) = 1 - P(Z<2.67)

P(X>140) = 1 - 0.9082

P(X>140) = 0.0918

Percentage = 9.18%

Therefore 9.18% of people has an iq over 120.

To learn more about normal distribution visit:

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