Math Problem Statement

A poll showed that 67.3% of Americans say they believe that statistics teachers know the true meaning of life. What is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life.

Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.

Solution

The percentage of Americans who do not believe that statistics teachers know the true meaning of life is the complement of those who do. This can be found by subtracting the percentage of believers from 100%.

Percentage of non-believers=100%67.3%=32.7%\text{Percentage of non-believers} = 100\% - 67.3\% = 32.7\%

Thus, the probability of randomly selecting someone who does not believe is 32.7.

Would you like further details or explanations?

Here are five related questions:

  1. What is the complement rule in probability?
  2. How do you calculate the probability of two independent events?
  3. What is the difference between relative frequency and probability?
  4. How do you calculate probabilities from a normal distribution?
  5. How can sample size affect the accuracy of polls?

Tip: In probability, the complement of an event is the likelihood that the event does not occur, calculated by subtracting the event's probability from 1.

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Math Problem Analysis

Mathematical Concepts

Complement Rule
Probability

Formulas

Complement Probability Formula: P(A') = 1 - P(A)

Theorems

Complement Rule in Probability

Suitable Grade Level

Grades 6-8