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Chapter 10: Problem 5

Suppose that your lab scores in a biology class were 61 out of 75 points in Lab 1,17 out of 20 points in Lab 2 , and 118 out of 150 in Lab 3. Compare your lab scores and rank them in order, from best to last.

Short Answer

Expert verified
The ranked lab scores from best to last are: Lab 2, Lab 1, Lab 3.

Step by step solution

01

Calculate the Percentage for Lab 1

To make comparisons possible, we first convert all the scores into percentages. For Lab 1, the percentage score is calculated by dividing the achieved score by the total score and then multiplying by 100. Therefore, the percentage for Lab 1 is given by: \( \frac{61}{75} \times 100 = 81.33 \% \)
02

Calculate the Percentage for Lab 2

Following the same procedure, for Lab 2: \( \frac{17}{20} \times 100 = 85 \% \)
03

Calculate the Percentage for Lab 3

And finally, for Lab 3: \( \frac{118}{150} \times 100 = 78.67 \% \)
04

Ranking the Lab Scores

Now that we have all results in percentages, we can rank them from best to last. The lab with the highest percentage is ranked first, and the one with the lowest percentage is ranked last. In this case, thus, the ranking is: Lab 2 (85%), Lab 1 (81.33%), and Lab 3 (78.67%)

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Key Concepts

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

Percentage Calculation
Understanding how to calculate percentages is essential in evaluating scores, such as those from lab assessments. The percentage tells us how well you performed relative to the total possible score.
  • To calculate a percentage, you divide the score you got by the total score possible.
  • Then, multiply the result by 100 to convert it into a percentage.
For example, in Lab 1, where you scored 61 out of a possible 75 points, the calculation would be: \[ \frac{61}{75} \times 100 = 81.33\% \]This tells us that you earned 81.33e percent of the total possible points for Lab 1.
Ranking Scores
Once you've converted scores into percentages, ranking them becomes straightforward.
  • The percentage enables you to make a uniform comparison across different tests or assignments, regardless of their total score.
  • Ranks tell us the order of the scores from highest to lowest, providing clarity on performance.
For our labs, Lab 2 had the highest percentage score, followed by Lab 1, and then Lab 3. This ranking helps you quickly identify which lab performance was your best and which was your weakest.
Lab Score Comparison
Comparing lab scores in percentage form is more enlightening and accurate than simply comparing raw scores. Imagine having different total possible points for each lab, like in our example:
  • Lab 1: 61 out of 75
  • Lab 2: 17 out of 20
  • Lab 3: 118 out of 150
By converting these to percentages, you achieve a standardization that allows for direct comparison:
  • Lab 1: 81.33%
  • Lab 2: 85%
  • Lab 3: 78.67%
This comparison highlights that even if the raw scores seem different, the percentage gives an accurate picture of relative performance.
Basic Math Skills
Basic math skills form the foundation of these calculations and are crucial for academic success.
  • Understanding fractions is critical as percentages are often derived from them.
  • Multiplication and division play key roles in these computations.
Strengthening these skills not only helps in your current studies but also prepares you for more advanced mathematical challenges. It's beneficial to regularly practice converting scores and doing these calculations to build confidence in your math abilities.

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Most popular questions from this chapter

Consider a CD paying a \(3.6 \%\) APR compounded continuously. Find the future value of the CD if you invest \(\$ 3250\) for a term of 1000 days. Round your answer to the nearest dollar.

A 250 -piece puzzle is missing \(14 \%\) of its pieces from its box. How many pieces are in the box?

Suppose you purchase a car and you are going to finance \(\$ 14,500\) for 36 months at an APR of \(6 \%\) compounded monthly. Find the monthly payments on the loan.

Jefferson Elementary School has 750 students. The Friday before spring break \(22 \%\) of the student body was absent. How many students were in school that day?

According to a Philadelphia Inquirer finance column, "Borrow \(\$ 100,000\) with a \(6 \%\) fixed-rate mortgage and you'll pay nearly \(\$ 116,000\) in interest over 30 years. Put an extra \(\$ 100\) a month into principal payments and you'd pay just \(\$ 76,000-\) and be done with mortgage payments nine years earlier." (鈥淎re Extra Mortgage Payments Good Idea?" in Philadelphia Inquirer. Copyright @ 2012 by Philadelphia Inquirer. Used by permission of Philadelphia Inquirer.) (a) Verify that the increase in the monthly payment that is needed to pay off the mortgage in 21 years is indeed close to \(\$ 100\) and that roughly \(\$ 40,000\) will be saved in interest. (b) How much should the monthly payment be increased so as to pay off the mortgage in 15 years? How much interest is saved in doing so? (c) How much should the monthly payment be increased so as to pay off the mortgage in \(t\) years \((t<30) ?\) Express the answer in terms of \(t\)
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