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Chapter 5: Problem 50

Conduct a survey in your school by randomly asking 50 students whether they drive to school. Based on the results of the survey, approximate the probability that a randomly selected student drives to school.

Short Answer

Expert verified
Probability is \( \frac{X}{50} \)

Step by step solution

01

Conduct the Survey

Ask 50 randomly selected students at your school whether they drive to school. Record the number of students who answer 'yes.'
02

Count the Positive Responses

Count the number of students who responded 'yes' to driving to school. Let this number be referred to as 'X.'
03

Calculate the Probability

Use the formula for probability: \( P(\text{drive to school}) = \frac{X}{50} \) Divide the number of students who said 'yes' (X) by the total number of students surveyed (50) to get the probability.

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Key Concepts

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

Random Sampling
Random sampling is a method used to select a subset of individuals from a larger population. The goal is to ensure that each individual in the population has an equal chance of being chosen.
This is crucial to avoid bias in your survey results and to make sure that your findings accurately represent the larger group. For example, in our exercise, you randomly ask 50 students out of the entire school population.
By doing this, you are more likely to get a balanced mix of responses. This makes your data more reliable and gives a better approximation of the probability you aim to calculate.
Data Collection
Data collection is gathering information from your sample. In our case, you asked students whether they drive to school and recorded their responses.
This step is essential because the accuracy of your results heavily depends on how you collect your data. Here are some tips for effective data collection:
  • Ensure anonymity to get honest answers.
  • Be consistent in how you ask each question.
  • Record the responses accurately.
Misrecording or inconsistencies can lead to errors that skew your survey results.
Probability Calculation
Probability Calculation involves using the data you collected to determine the likelihood of a specific outcome. In this exercise, you're trying to find out how likely it is that a randomly selected student drives to school.
The formula used is simple and straightforward:

\[ P(\text{drive to school}) = \frac{X}{50} \]
Here 'X' is the number of students who said 'yes.' For example, if 20 out of 50 students said they drive to school, your probability is:
\[ P(\text{drive to school}) = \frac{20}{50} = 0.4 \]
This means there is a 40% chance that a randomly selected student drives to school.
Understanding probability helps in making informed decisions based on statistical data.

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Most popular questions from this chapter

Adult Americans (18 years or older) were asked whether they used social media (Facebook, Twitter, and so on ) regularly. The following table is based on the results of the survey. $$ \begin{array}{lccccc} & \mathbf{1 8 - 3 4} & \mathbf{3 5 - 4 4} & \mathbf{4 5 - 5 4} & \mathbf{5 5 +} & \text { Total } \\ \hline \begin{array}{l} \text { Use social } \\ \text { media } \end{array} & 117 & 89 & 83 & 49 & \mathbf{3 3 8} \\ \hline \begin{array}{l} \text { Do not use } \\ \text { social media } \end{array} & 33 & 36 & 57 & 66 & \mathbf{1 9 2} \\ \hline \text { Total } & \mathbf{1 5 0} & \mathbf{1 2 5} & \mathbf{1 4 0} & \mathbf{1 1 5} & \mathbf{5 3 0} \\ \hline \end{array} $$ (a) What is the probability that a randomly selected adult American uses social media, given the individual is \(18-34\) years of age? (b) What is the probability that a randomly selected adult American is \(18-34\) years of age, given the individual uses social media? (c) Are 18 - to 34 -year olds more likely to use social media than individuals in general? Why?

A combination lock has 50 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. Repetitions are allowed.

List all the combinations of four objects \(a, b, c,\) and \(d\) taken two at a time. What is \({ }_{4} C_{2} ?\)

Suppose that you just received a shipment of six televisions and two are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability that at least one does not work?

Lingo In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers corresponding to the numbers remaining on their Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses their second draw. To form a Lingo, the team needs five numbers in a vertical, horizontal, or diagonal row. Consider the sample Lingo board below for a team that has just guessed a mystery word. $$ \begin{array}{|l|l|l|l|l|} \hline \mathbf{L} & \mathbf{I} & \mathbf{N} & \mathbf{G} & \mathbf{O} \\ \hline 10 & & & 48 & 66 \\ \hline & & 34 & & 74 \\ \hline & & 22 & 58 & 68 \\ \hline 4 & 16 & & 40 & 70 \\ \hline & 26 & 52 & & 64 \\ \hline \end{array} $$ (a) What is the probability that the first ball selected is on the Lingo board? (b) What is the probability that the team draws a stopper ball on its first draw? (c) What is the probability that the team makes a Lingo on their first draw? (d) What is the probability that the team makes a Lingo on their second draw?
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