29​% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is​ (a) exactly​ two, (b) more than​ two, and​ (c) between two and​ five, inclusive. 
Question content area bottom
Part 1
​(a) P(2)equals=enter your response here ​(Round to the nearest thousandth as​ needed.) 

This problem involves a **binomial distribution**, as we are looking at a fixed number of trials (10 adults), two possible outcomes for each trial (whether an adult is more likely to make purchases during a sales tax holiday or not), and a constant probability of success (29% or 0.29).

### Formula for Binomial Probability:

\[
P(x) = \binom{n}{x} p^x (1 - p)^{n - x}
\]

Where:
- \( n = 10 \) (the number of adults),
- \( p = 0.29 \) (the probability that an adult is more likely to make a purchase),
- \( x \) is the number of successes (adults who will make a purchase during the sales tax holiday),
- \( \binom{n}{x} \) is the combination formula \( \binom{n}{x} = \frac{n!}{x!(n-x)!} \).

### (a) Probability that exactly 2 adults are more likely to make a purchase:

We need to find \( P(2) \).

\[
P(2) = \binom{10}{2} (0.29)^2 (1 - 0.29)^{10 - 2}
\]

Now, I'll compute the value.The probability that exactly 2 adults are more likely to make a purchase during a sales tax holiday is approximately **0.244** (rounded to the nearest thousandth).

Do you want details or have any questions?

Here are five related questions that build on this concept:
1. How do you calculate binomial probabilities for different values of \(x\)?
2. What happens to the probability if the number of trials \(n\) increases?
3. How would the probability change if the percentage of adults likely to make purchases was 40% instead of 29%?
4. What is the expected number of adults out of 10 who would make a purchase during a sales tax holiday?
5. How can you use a binomial distribution table to find probabilities for different values?

**Tip**: In binomial distributions, the probability of "success" can be thought of as the likelihood of an event happening in a single trial, and the number of trials determines how often you test for that event.

29​% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is​ (a) exactly​ two, (b) more than​ two, and​ (c) between two and​ five, inclusive.

This problem calculates the binomial probability for U.S. adults who are more likely to make purchases during a sales tax holiday, given that 29% of adults fit this description. Learn how to compute probabilities for exactly 2, more than 2, and between 2 and 5 adults in a sample of 10. Suitable for 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