Answer:
The minimum score a person must have to qualify for the society is 162.05
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 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:
Test scores are normally distributed with a mean of 140 and a standard deviation of 15. This means that .
What is the minimum score a person must have to qualify for the society?
Since the person must score in the upper 7% of the population, this is the X when Z has a pvalue of 0.93.
This is .
So
The minimum score a person must have to qualify for the society is 162.05