Answer:
Q1 = 89.1525
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:

Find the first quartile Upper Q 1Q1, which is the IQ score separating the bottom 25% from the top 75%
This is the value of X when Z has a pvalue of 0.25. So it is X when Z = -0.675.




So
Q1 = 89.1525