Math Problem Statement

A school newspaper reporter decides to randomly survey 11 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 20% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. In words, define the Random Variable X.

the types of festivities offered at the schoolthe school newspaper    the number of students in the schoolthe number of students that will attend Tet

Solution

The random variable XX is defined as the number of students who will attend Tet (Vietnamese New Year) festivities this year, out of the 11 students randomly surveyed.

In words:

XX: The number of students from the 11 surveyed who will attend the Tet festivities.

Since it's a random variable, it takes integer values from 0 to 11, with each value representing the number of students who will attend the festivities.


Would you like me to help with the probability distribution or any further analysis on this situation?

Here are 5 related questions for further exploration:

  1. How do we calculate the probability of exactly 3 students attending Tet festivities?
  2. What type of probability distribution does XX follow, and why?
  3. What is the expected number of students who will attend Tet festivities based on the given probability?
  4. How would the result change if the probability of attending Tet festivities increased to 30%?
  5. How can we compute the standard deviation for the number of students attending Tet?

Tip: When dealing with random variables, it’s important to first identify the possible outcomes (like the number of attendees) and their associated probabilities. This helps in constructing the right probability distribution!

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Math Problem Analysis

Mathematical Concepts

Probability
Random Variables
Binomial Distribution

Formulas

Binomial Probability Formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Theorems

Law of Large Numbers
Binomial Distribution Theorem

Suitable Grade Level

Grades 9-11