In a study of environmental lead exposure and IQ, the data was collected from 148 children in Boston, Massachusetts. Their IQ score an age 10 approximately follow a normal distribution with a mean of 115.9 and standard deviation of 14.2. Suppose one child had an IQ of 74. A) Calculate the lower fence for the IQ data, which is the lower limit value that the IQ score can be without being considered an outlier.B) Then, calculate the probability of obtaining an IQ score value of 74 or less.

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Asked May 5, 2019
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In a study of environmental lead exposure and IQ, the data was collected from 148 children in Boston, Massachusetts. Their IQ score an age 10 approximately follow a normal distribution with a mean of 115.9 and standard deviation of 14.2. Suppose one child had an IQ of 74. 

A) Calculate the lower fence for the IQ data, which is the lower limit value that the IQ score can be without being considered an outlier.

B) Then, calculate the probability of obtaining an IQ score value of 74 or less.

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Expert Answer

Step 1

Denote X as the IQ scores. It is given that X is normally distributed, with mean μ = 115.9 and standard deviation σ = 14.2. It is assumed that a child has an IQ score of 74.

Step 2

A) Calculating the lower fence of IQ data:

The lower fence for the data is given by the formula:

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Step 3

It is assumed that a child has an IQ score of 74. Therefore, lower fence of IQ data, which is the lower li...

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