In a study of environmental lead exposure and IQ, the data was collected from 148 children...

In a study of environmental lead exposure and IQ, the data was collected from 148 children in Boston, Massachusetts. Their IQ scores at age of 10 approximately follow a normal distribution with mean of 115.9 and standard deviation of 14.2.Suppose one child had an IQ of 74. The researchers would like to know whether an IQ of 74 is an outlier or not.

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. Keep a precision level of two decimal places for the lower fence.

Then, calculate the probability of obtaining an IQ score value of 74 or less. Keep a precision level of four decimal places for the probability.

probability of IQ score less than the lower fence:

Expert Solution

Lower fence for outlier is if Z - score corresponds to IQ is less than -3

µ = 115.9
σ = 14.2

z=(x-µ)/σ
so, X=zσ+µ=   -3.000   *   14.2   +   115.9
X   =   73.3
so, lower fence = 73.3

since, 74 is above the lower fence, so, it is not an outlier

-----------------------------------------

µ =    115.9
σ =    14.2
left tailed
P( X ≤    74   )

Z =(X - µ ) / σ = (   74   -   115.9   ) /    14.2
Z =    -2.951
P(X ≤   74   ) = P(Z ≤   -2.951   ) =   0.0016
excel formula for probability from z score is =NORMSDIST(Z)

orchestra answered 2 years ago

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