Answered

Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Our experts provide timely and precise responses to help you understand and solve any issue you face.

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 25 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?

Sagot :

Using the normal distribution, it is found that a student has to score 0.675 standard deviations above the mean to be publicly recognized.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • 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 25% is at least the 100 - 25 = 75th percentile, which is X when z has a p-value of 0.75.

  • Looking at the z-table, z = 0.675 has a p-value of 0.75.

Hence, a student has to score 0.675 standard deviations above the mean to be publicly recognized.

A similar problem is given at https://brainly.com/question/25784380

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.