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Chapter 3: Problem 123

Melissa's grade in her math class is determined by three 100 -point tests and a 200 -point final exam. To determine the grade for a student in this class, the instructor will add the four scores together and divide this sum by 5 to obtain a percentage. This percentage must be at least 80 for a grade of \(\mathrm{B}\). If Melissa's three test scores are 75,69 , and 87 , what is the minimum score she needs on the final exam to obtain a B grade?

Short Answer

Expert verified
Melissa needs a minimum score of 169 on the final exam to get a B grade.

Step by step solution

01

Calculate the Total Points Earned So Far

To calculate the total points earned so far, sum up Melissa's three test scores. In this case, \(75 + 69 + 87 = 231\) points.
02

Setup the Equation

Melissa needs an average of 80 from all these scores. Since the total is divided by 5 to obtain this average, Melissa needs \(80 \times 5 = 400\) points in total. Let's denote the score for Melissa's final exam as \(x\). So our equation becomes \(231 + x = 400\).
03

Solve for x

Solve the equation for \(x\) to get Melissa's minimum required score on the final. Subtract 231 from both sides of the equation to get \(x = 400 - 231 = 169\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mathematics
Mathematics is a broad field dealing with numbers, quantities, and shapes. It involves understanding and manipulating different concepts to solve problems. In this exercise, Melissa's grade is determined using mathematical calculations.

It requires addition, multiplication, and subtraction to determine the result. Mathematics teaches us logical thinking and problem-solving skills, which are essential in daily life.

Being comfortable with basic math operations is crucial, especially when determining grades and understanding academic performance.
Final Exam
The final exam in this exercise is crucial for Melissa's grade. It is a significant assessment that contributes 200 points to the overall score.

A final exam usually covers material from the entire course, testing a student's overall understanding and retention of the subject matter.
  • Typically, it has a greater weight compared to other tests in the grading system.
  • It challenges students to apply all learned concepts effectively.
Understanding how much final exams count towards a grade helps students prioritize their study efforts.
Test Scores
Test scores are a numerical representation of a student's performance. In Melissa's case, each of her three tests was scored out of 100.

Test scores provide feedback on how well a student understands particular subjects or topics.

They are crucial in determining a student's final grade. While individual test scores may vary, it's the cumulative effect that impacts the overall outcome significantly.

Keeping track of test scores helps in knowing where you stand and what areas you might need to improve in before the final exam.
Percentage
A percentage is a way to express a number as a fraction of 100. In Melissa's case, her grade is expressed as a percentage of the total possible points.

To calculate the percentage needed for a particular grade, the total points are divided by the factor that results in 100 if the percentage is achieved.
  • In this exercise, Melissa's scores are added and then divided by 5 to determine the percentage.
  • The grade boundaries are set, such as at least an 80% for a B grade.
Understanding how to calculate percentages helps students know exactly what is required to achieve a specific grade.

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Most popular questions from this chapter

Refer to Exercise \(2.94\), which listed the alcohol content by volume for each of the 13 varieties of beer produced by Sierra Nevada Brewery. Those data are reproduced here: \(\begin{array}{llllllllll}4.4 & 5.0 & 5.0 & 5.6 & 5.6 & 5.8 & 5.9 & 5.9 & 6.7 & 6.8\end{array}\) \(\begin{array}{lll}6.9 & 7.0 & 9.6\end{array}\) Calculate the range, variance, and standard deviation.

Nixon Corporation manufactures computer monitors. The following are the numbers of computer monitors produced at the company for a sample of 30 days: \(\begin{array}{llllllllll}24 & 32 & 27 & 23 & 33 & 33 & 29 & 25 & 23 & 28 \\\ 21 & 26 & 31 & 20 & 27 & 33 & 27 & 23 & 28 & 29 \\ 31 & 35 & 34 & 22 & 26 & 28 & 23 & 35 & 31 & 27\end{array}\) Prepare a box-and-whisker plot. Comment on the skewness of these data.

A small country bought oil from three different sources in one week, as shown in the following table. \begin{tabular}{lcc} \hline Source & Barrels Purchased & Price per Barrel (\$) \\ \hline Mexico & 1000 & 95 \\ Kuwait & 200 & 92 \\ Spot Market & 100 & 99 \\ \hline \end{tabular}

Jeffrey is serving on a six-person jury for a personal-injury lawsuit. All six jurors want to award damages to the plaintiff but cannot agree on the amount of the award. The jurors have decided that each of them will suggest an amount that he or she thinks should be awarded; then they will use the mean of these six numbers as the award to recommend to the plaintiff. a. Jeffrey thinks the plaintiff should receive \(\$ 20,000\), but he thinks the mean of the other five jurors' recommendations will be about \(\$ 12,000 .\) He decides to suggest an inflated amount so that the mean for all six jurors is \(\$ 20,000\). What amount would Jeffrey have to suggest? b. How might this jury revise its procedure to prevent a juror like Jeffrey from having an undue influence on the amount of damages to be awarded to the plaintiff?

Refer to Exercise 3.97. The following data represent the credit scores of 22 randomly selected loan applicants. \(\begin{array}{lllllllllll}494 & 728 & 468 & 533 & 747 & 639 & 430 & 690 & 604 & 422 & 356 \\ 805 & 749 & 600 & 797 & 702 & 628 & 625 & 617 & 647 & 772 & 572\end{array}\) Prepare a box-and-whisker plot. Are these data skewed in any direction?
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