An employer has applicants take a short exam when applying to a job opening. One of their criteria is that the applicant must score in the top 2.5% of all applicants who took the exam. The exam is constructed such that the scores are normally distributed with an average of 58 and a standard deviation of 7.

Applicants need a score of at least 71.72.

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:

Top 2.5%.

Scores that are X when Z has a pvalue of 1-0.025 = 0.975 and higher. So it is scores that are X when Z = 1.96 and higher.

Applicants need a score of at least 71.72.

eveidence i thing that

step-by-step explanation:

the answer is 5636.7