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? (Round your answer to 2 decimal places.)

Answer 1

Answer:

The scores above 1.08 standard deviation from the mean are publicly recognized.

Step-by-step explanation:

We are given the following information in the question:

Mean = μ

Standard Deviation = σ

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.14

$P( X > x) = P( z > \displaystyle\frac{x - \mu}{\sigma})=0.14$  

$= 1 -P( z \leq \displaystyle\frac{x - \mu}{\sigma})=0.14$  

$=P( z \leq \displaystyle\frac{x - \mu}{\sigma})=0.86$  

Calculation the value from standard normal z table, we have,  

$\displaystyle\frac{x - \mu}{\sigma} = 1.08\\\\x =\mu + 1.08\sigma$  

Thus, scores above 1.08 standard deviation from the mean are publicly recognized.