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Answer:
The inter-decile range of IQ is 40.96.
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:
First decile:
100/10 = 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
Ninth decile:
9*(100/10) = 90th percentile, which is X when Z has a pvalue of 0.9. So it is X when Z = 1.28.
Interdecile range:
120.48 - 79.52 = 40.96
The inter-decile range of IQ is 40.96.