A poll found that 30​% of adults do not work at all while on summer vacation. In a random sample of 5 ​adults, let X represent the number who do not work during summer vacation.  Give the value of p for this experiment

In this scenario, \( X \) represents the number of adults who do not work during summer vacation, in a random sample of 5 adults. This can be modeled as a **binomial distribution**, where each adult has a probability of either not working or working during vacation. 

The value of \( p \) is the probability of an individual adult not working during summer vacation.

From the information given:

- 30% of adults do not work on vacation.
  
So, the probability \( p \) is:

\[
p = 0.30
\]

This means the probability of success (an adult not working) in each trial is 0.30.

Let me know if you need further clarifications or additional details.

Here are five related questions to further explore this topic:
1. What is the probability that exactly 3 adults do not work during summer vacation in this sample?
2. What is the probability that at least 1 adult does not work during summer vacation in this sample?
3. How would the probability change if the sample size increased to 10 adults?
4. What is the expected number of adults who do not work during summer vacation?
5. What is the variance of the number of adults who do not work during summer vacation?

**Tip:** When dealing with binomial distributions, the parameters are \( n \) (the number of trials) and \( p \) (the probability of success in each trial). These parameters define the entire distribution.

A poll found that 30% of adults do not work at all while on summer vacation. In a random sample of 5 adults, let X represent the number who do not work during summer vacation. Give the value of p for this experiment.

Explore how to determine the probability (p) in a binomial distribution scenario where 30% of adults do not work during summer vacation. This problem involves key probability concepts, including binomial distribution, and is suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation