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Chapter 5: Problem 4

On average, the campus shuttle bus passes the library about once every hour.

Short Answer

Expert verified
The probability of the campus shuttle bus passing by the library at a specific minute during an hour is \(\frac{1}{60}\) or approximately 1.67%.

Step by step solution

01

Understanding the given data

We have the average frequency of the campus shuttle bus, which is once every hour. So, the shuttle bus passes by the library once in one hour (60 minutes).
02

Calculate the probability of the bus passing at a particular minute

Since there are 60 minutes in an hour and the bus passes by the library once in that hour, the probability of the bus passing at any given minute can be calculated as follows: Probability of bus passing at a particular minute = 1/total minutes in an hour Plug the values into the equation: \( Probability = \frac{1}{60} \)
03

Represent the probability as a percentage or a fraction

The probability can be represented as a fraction or a percentage. To convert the probability from a fraction to a percentage, multiply it by 100. Percentage Probability = Probability * 100 \( Percentage Probability = \frac{1}{60} * 100 \) Percentage Probability = 1.67% (approximately) Thus, the probability of the campus shuttle bus passing by the library at a specific minute is 1/60 or 1.67% during an hour.

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Key Concepts

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

Statistics
Statistics is a branch of mathematics dealing with data collection, analysis, interpretation, presentation, and organization. It provides us tools to transform raw data into meaningful information. When discussing probabilities, statistical data can help in predicting how often an event might occur.
  • In the context of the shuttle bus frequency, statistical analysis is used to determine the average number of times the shuttle bus passes the library.
  • This average is vital because it allows us to calculate probabilities鈥攍ike the likelihood of the bus passing by at a given minute.
Statistics gives us a way to understand and describe the likelihood of events based on observed data, helping in informed decision-making.
Fraction to Percentage Conversion
Fraction to percentage conversion is a crucial skill in understanding data and probabilities better. To convert a fraction to a percentage, you multiply the fraction by 100. This conversion helps in expressing the probability in a form that is easier for many people to understand. For example, the probability that the shuttle bus passes at any given minute is expressed as a fraction \( \frac{1}{60} \).
  • To convert \( \frac{1}{60} \) into a percentage, you perform the calculation: \( \frac{1}{60} \times 100 \).
  • This results in approximately 1.67%.
Representing the probability as a percentage helps in visualizing how small the likelihood is within the context of an hour.
Probability Representation
Probability representation is the expression of likelihood that a particular event will occur, often represented as a fraction or a percentage. It helps you to understand the extent of chances associated with an event.In our shuttle bus scenario:
  • The probability of the bus passing by the library at any specific minute is represented as \( \frac{1}{60} \) or approximately 1.67%.
Different representations鈥攚hether fractions or percentages鈥攐ffer flexibility in how we present statistical information, enabling clearer communication. By using these representations, you can easily compare and understand probabilities in real-life scenarios, improving your analytical skills.

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