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UNO [17]
2 years ago
8

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capa

bility 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?
Mathematics
1 answer:
erica [24]2 years ago
6 0

Using the normal distribution, it is found that a student has to score 0.6433 standard deviations above the mean to be publicly recognized.

<h3>Normal Probability Distribution</h3>

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

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