Answer:
The minimum score needed to be in the top 5% of the scores on the test is 172.9.
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:
What is the minimum score needed to be in the top 5% of the scores on the test?
The 100-5 = 95th percentile, which is the value of X when Z has a pvalue of 0.95. So it is X when Z = 1.645.
The minimum score needed to be in the top 5% of the scores on the test is 172.9.
