56.27 in expanded form
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Answer:
So the z-scores that separate the unusual IQ scores from those that are usual are Z = -2 and Z = 2.
The IQ scores that separate the unusual IQ scores from those that are usual are 84 and 148.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
What are the z scores that separate the unusual IQ scores from those that are usual?
If Z<-2 or Z > 2, the IQ score is unusual.
So the z-scores that separate the unusual IQ scores from those that are usual are Z = -2 and Z = 2.
What are the IQ scores that separate the unusual IQ scores from those that are usual?
Those IQ scores are X when Z = -2 and X when Z = 2. So
Z = -2
Z = 2
The IQ scores that separate the unusual IQ scores from those that are usual are 84 and 148.