Answer:
A person must get an IQ score of at least 138.885 to qualify.
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 problem, we have that:
(a). [7pts] What IQ score must a person get to qualify
Top 8%, so at least the 100-8 = 92th percentile.
Scores of X and higher, in which X is found when Z has a pvalue of 0.92. So X when Z = 1.405.
A person must get an IQ score of at least 138.885 to qualify.