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In a survey of 1100 female adults (18 years of age or older), it was determined that 341 volunteered at least once in the past year. (a) What is the probability that a randomly selected adult female volunteered at least once in the past year? (b) Interpret this probability.

Short Answer

Expert verified
The probability is approximately 0.3109 or 31.09%. This means there's about a 31.09% chance that a randomly selected adult female volunteered at least once in the past year.

Step by step solution

01

- Determine Total Number of Female Adults Surveyed

Identify the total number of adult females who participated in the survey. From the given information, this number is 1100.
02

- Determine Number of Female Adults Who Volunteered

Identify the number of adult females who volunteered at least once in the past year. From the given information, this number is 341.
03

- Calculate the Probability

Use the probability formula: \[ P(A) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]Here, the number of favorable outcomes is the number of females who volunteered (341), and the total number of outcomes is the total number of surveyed females (1100). Thus,\[ P(V) = \frac{341}{1100} \approx 0.3109 \].
04

- Interpret the Probability

The probability of approximately 0.3109 means that there is about a 31.09% chance that a randomly selected adult female from the survey volunteered at least once in the past year.

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Key Concepts

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

Probability
Probability helps you understand how likely an event is to happen. In this exercise, we want to know the probability that a randomly chosen adult female has volunteered at least once in the past year.
To find the probability, you use this formula: \[ P(A) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \] Here:
  • The 'Number of Favorable Outcomes' is the number of females who volunteered, which is 341.
  • The 'Total Number of Outcomes' is the total number of surveyed females, which is 1100.

Plug these numbers into the formula to get: \[ P(V) = \frac{341}{1100} \ P(V) = 0.3109 \] So, there is a 31.09% chance that a randomly chosen female adult from the survey volunteered at least once in the past year. Probability ranges from 0 to 1. A probability of 0 means an event will not happen at all, and a probability of 1 means it will definitely happen.
Survey Data Analysis
Survey data analysis is about understanding the information collected through surveys.
This involves identifying the total number of participants and the specific number of participants with certain characteristics. In this case, the survey involved 1100 adult females.
Among these surveyed females, 341 indicated they volunteered at least once in the past year.
It is important to:
  • Know your sample size – here it is 1100.
  • Identify the subgroup you are interested in – here it is those who volunteered, which is 341.
By analyzing survey data, you can make important decisions or conclusions based on the collected responses. The percentages or probabilities derived from such data help in understanding and predicting behaviors and opinions. It is a way to make sense of raw data.
Interpreting Statistical Results
Interpreting statistical results means explaining what the numerical findings mean in a real-world context. In this exercise, we calculated that the probability of a randomly selected adult female being a volunteer in the past year is about 0.3109 or 31.09%.
This means that if you randomly select one adult female from the surveyed group, there’s a little over 31% chance she volunteered. It's essential to translate these numbers into meaningful insights.
Here’s how you can do it:
  • Understand the statistic – here, it’s a probability of 31.09%.
  • Relate it to the real world – it shows how common volunteering is within this group.
  • Communicate the findings clearly – for example, 'About 31 out of every 100 adult females volunteered at least once last year.'

These interpretations help turn figures into actionable knowledge, useful for further research, planning volunteer programs, or encouraging community participation.

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