The lowest score you can earn and still be eligible for employment is 85.6925.
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 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:
Top 5%.
At least the 100-5 = 95th percentile.
The 95th percentile is X when Z has a pvalue of 0.95. So X when Z = 1.645.
x-75 = 1.645*6.5
x = 85.692
Thus the lowest score you can earn and still be eligible for employment is 85.6925.
Learn more about Standard Deviation on:
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