In a recent​ poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. If a survey of a random sample of 15 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral​ values. In 100 trials of this​ experiment, we expect about ? to result in exactly 88 adults who feel the state of morals is poor.

In this problem, we are dealing with a **binomial distribution**, where:

- The probability of success (i.e., an adult believing the state of moral values is poor) is \( p = 0.45 \).
- The number of trials (adults in the survey) is \( n = 15 \).
- We are interested in the probability of exactly \( k = 88 \) adults believing that the state of moral values is poor.

However, there is a crucial issue here: you're conducting a survey of only 15 adults, and the question asks about the probability of exactly **88** adults believing the state of morals is poor. Since \( 88 > 15 \), it's impossible for 88 people out of 15 to believe something.

Thus, the probability of this event is **zero** (impossible), meaning we would expect **zero** trials in 100 trials to result in exactly 88 adults who feel the state of morals is poor.

### Would you like details on binomial distribution, or have other questions?
Here are 5 questions related to this topic:

1. What is the formula for calculating binomial probability?
2. How can you calculate the probability of exactly 8 out of 15 adults believing morals are poor?
3. What assumptions are made in binomial distribution?
4. How would increasing the sample size impact the probability calculations?
5. What other types of distributions are used in probability theory?

**Tip:** When dealing with a binomial distribution, always check that the number of successes you're looking for is within the range of possible outcomes (between 0 and \( n \)).

In a recent​ poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. If a survey of a random sample of 15 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral​ values, in 100 trials of this experiment, we expect about ? to result in exactly 88 adults who feel the state of morals is poor.

Explore how to calculate binomial probability in a random survey of 15 adults with a success probability of 0.45. This example addresses a common misinterpretation of survey data and covers the binomial distribution formula and theorem. Suitable for high school students, Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation