Answer:
IQ score of 102.55
Step-by-step explanation:
Problems of normally distributed samples can be 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, which is also the shaded area under the curve, 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:
The shaded area under the curve is 0.5675.
This means that Z has a pvalue of 0.5675.
So, we have to find X when Z = 0.17.
IQ score of 102.55