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 26 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 0.6433 standard deviations above the mean to be publicly recognized.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the 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 26% of the scores are given by scores above the 74th percentile, which corresponds to Z = 0.6433, hence, a student has to score 0.6433 standard deviations above the mean to be publicly recognized.

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