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In a study of environmental lead exposure and IQ, the data was collected from 160160 children...

In a study of environmental lead exposure and IQ, the data was collected from 160160 children in Cleveland, Ohio. Their IQ scores at age of 44 approximately follow a normal distribution with mean of 86.786.7 and standard deviation of 16.2.16.2. Suppose one child had an IQ of 135.135. The researchers would like to know whether an IQ of 135135 is an outlier or not.

Calculate the upper fence for the IQ data, which is the upper limit value that the IQ score can be without being considered an outlier. Keep a precision level of two decimal places for the upper fence.

Then, calculate the probability of obtaining an IQ score value of 135135 or greater. Keep a precision level of four decimal places for the probability.

probability of IQ score greater than the upper fence:

math   Statistics-And-Probability   
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Answer #1

Let X is a random variable shows the IQ score. Here X has normal distribution with following parameters

For a normal distribution, scores that are not within three standard deviations of mean considered as outliers.

The upper fence will be

Upper fence: 135.30

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The z-score for X = 135 is

The probability of obtaining an IQ score value of 135 or greater is

Answer: 0.0014

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