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 8 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.)
<u>The correct answer is that a student have to score 1.41 standard deviations above the mean to be publicly recognized.</u>
Step-by-step explanation:
For answering the question, we don't know the score mean of the National Financial Capability Challenge Exam and neither the population or number of students who take the exam. The only information provided is that the public recognition in this normal distribution is only for students that scores in the top 8%. In other words for students above 92% of the population.
With this information, we can go to a Z Score Table and check that for being on the top 8% (above the 92% of any population), your result must be 1.405 standard deviations above the mean.
<u>Rounding the answer to 2 decimal places, it's 1.41 standard deviations above the mean.</u>
Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that . We are given the lengths of all 3 sides in terms of , but we only need to set two of them equal to each other to solve for . Let's use and to solve for . We know that , , and . Therefore, we can write the following equation to solve for
(Substitute given values into equation)
Solving for , we get:
(Subtract from both sides of the equation to isolate constants)
(Simplify)
(Subtract from both sides of the equation to isolate )
(Simplify)
(Divide both sides of the equation by to get rid of 's coefficient)