Question

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 14 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?

Answer 1

Using the normal distribution, it is found that a student has to score 1.08 standard deviations above the mean to be publicly recognized.

Normal Probability Distribution

In a normal distribution with mean $\mu$standard deviation $\sigma$z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It 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, which is the percentile of X.

The top 14% of the scores are given by scores above the 86th percentile, which corresponds to Z = 1.08, hence, a student has to score 1.08 standard deviations above the mean to be publicly recognized.

More can be learned about the normal distribution at brainly.com/question/24663213