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Chapter 3: Problem 138

Answer the following questions a. The total weight of all pieces of luggage loaded onto an airplane is 12,372 pounds, which works out to be an average of \(51.55\) pounds per piece. How many pieces of luggage are on the plane? b. A group of seven friends, having just gotten back a chemistry exam, discuss their scores. Six of the students reveal that they received grades of \(81,75,93,88,82\), and 85, respectively, but the seventh student is reluctant to say what grade she received. After some calculation she announces that the group averaged 81 on the exam. What is her score?

Short Answer

Expert verified
a. The total number of luggage pieces on the airplane is approximately 240. b. The score of the seventh student is 80.

Step by step solution

01

Calculate the total number of luggage pieces on the airplane

The average weight per luggage is given by dividing the total weight by the total number of luggage. So, to find the total number of luggage pieces loaded on the airplane, divide the total weight of all pieces of luggage \(12372\) pounds by the average weight per piece \(51.55\) pounds. Like this: \[ \text{Number of luggage pieces} = \frac{\text{Total weight}}{\text{Average weight per piece}} = \frac{12372}{51.55} \]
02

Calculate the score of the seventh student

First sum up the grades of the six students who have revealed their scores. Then subtract this sum from the total score of the group which is obtained by multiplying the group average (81) by the total number of students (7). Like this: \[ \text{Score of student 7} = \text{Total group score} - \text{Score of 6 students} = 7 \times 81 - (81+75+93+88+82+85) \]

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Key Concepts

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

Average Weight Calculation
When dealing with weight calculations, especially in context of logistics like loading luggage onto an airplane, understanding the concept of average is crucial. The average weight is computed by dividing the total weight by the number of items. In this case, the total weight of the luggage is 12,372 pounds. The average weight provided is approximately 51.55 pounds per piece. To find out how many pieces there are, you simply divide the total weight by the average weight.
  • Formula: \( \text{Total Number of Items} = \frac{\text{Total Weight}}{\text{Average Weight per Item}} \)
  • Calculation: \( \frac{12372}{51.55} \approx 240 \)
This tells us that there are around 240 pieces of luggage on the airplane. This type of calculation is extremely helpful when planning and organizing shipments to ensure weight limits are adhered to.
Total Number of Items
Understanding how to calculate the total number of items in a situation is a basic yet fundamental statistical skill. This calculation is critical when you have partial information, like an average, and need to determine total counts in various contexts. For instance, in the problem given, we needed to find the total number of luggage pieces based on total weight and average weight.
  • A clear step-by-step involving division of total by average provides the solution.
  • Helps in situations like inventory checks where you know the total volume/weight and average per item.
  • Also essential in budgeting and resource allocation to ensure all possibilities are covered efficiently.
Grasping this concept can save from estimation errors and facilitate better decision-making in logistics, retail, and any field requiring accurate inventory or resource tracking.
Student Exam Scores Analysis
Analyzing student exam scores involves understanding averages, totals, and sometimes individual contributions that may not be immediately visible. In the case where not all scores are known, determining an unknown score involves working backward from the group average and the known scores.
  • Firstly, multiply the average score by the number of students to find the total combined score.
  • Then subtract the sum of the known scores from this total to reveal the unknown score.
For the exercise, we know the group average is 81 for seven students. After calculation, the total score can be determined as \(7 \times 81 = 567\). Subtracting known scores: \(81 + 75 + 93 + 88 + 82 + 85 = 504\), we find the seventh student's score to be \(567 - 504 = 63\). Understanding this process allows students and educators to deduce missing information using available data effectively.

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Most popular questions from this chapter

A brochure from the department of public safety in a northern state recommends that motorists should carry 12 items (flashlights, blankets, and so forth) in their vehicles for emergency use while driving in winter. The following data give the number of items out of these 12 that were carried in their vehicles by 15 randomly selected motorists. \(\begin{array}{llllllllllllllll}5 & 3 & 7 & 8 & 0 & 1 & 0 & 5 & 1 & 21 & 07 & 6 & 7 & 1 & 19\end{array}\) Find the mean, median, and mode for these data. Are the values of these summary measures population parameters or sample statistics? Explain.

Consider the following two data sets. \(\begin{array}{llllrl}\text { Data Set I: } & 12 & 25 & 37 & 8 & 41 \\ \text { Data Set II: } & 19 & 32 & 44 & 15 & 48\end{array}\) Notice that each value of the second data set is obtained by adding 7 to the corresponding value of the first data set. Calculate the mean for each of these two data sets. Comment on the relationship between the two means.

Consider the following two data sets. \(\begin{array}{llllrl}\text { Data Set I: } & 12 & 25 & 37 & 8 & 41 \\ \text { Data Set II: } & 19 & 32 & 44 & 15 & 48\end{array}\) Note that each value of the second data set is obtained by adding 7 to the corresponding value of the first data set. Calculate the standard deviation for each of these two data sets using the formula for sample data. Comment on the relationship between the two standard deviations.

Seven airline passengers in economy class on the same flight paid an average of \(\$ 361\) per ticket. Because the tickets were purchased at different times and from different sources, the prices varied. The first five passengers paid \(\$ 420, \$ 210, \$ 333, \$ 695\), and \(\$ 485\). The sixth and seventh tickets were purchased by a couple who paid identical fares. What price did each of them pay?

The following data represent the numbers of tornadoes that touched down during 1950 to 1994 in the 12 states that had the most tornadoes during this period (Storm Prediction Center, 2009). The data for these states are given in the following order: CO, FL, IA, IL, KS, LA, MO, MS, NE, OK, SD, TX. \(\begin{array}{llllllllllll}1113 & 2009 & 1374 & 1137 & 2110 & 1086 & 1166 & 1039 & 1673 & 2300 & 1139 & 5490\end{array}\) a. Calculate the mean and median for these data. b. Identify the outlier in this data set. Drop the outlier and recalculate the mean and median. Which of these two summary measures changes by a larger amount when you drop the outlier? c. Which is the better summary measure for these data, the mean or the median? Explain.
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