d a breakup at least once during the last 10 years. Of nine randomly selected adults, find the probability that the number, X, who have years is m variable X. that you obtained in part (d) only approximately correct? What is the exact distribution called? ed a breakup at least once during the last 10 years is 0.109. s, inclusive, have experienced a breakup at least once during the last 10 years is 0.187. ability distribution of X. List the possible values of x in ascending order. 8 correct: 0
d a breakup at least once during the last 10 years. Of nine randomly selected adults, find the probability that the number, X, who have years is m variable X. that you obtained in part (d) only approximately correct? What is the exact distribution called? ed a breakup at least once during the last 10 years is 0.109. s, inclusive, have experienced a breakup at least once during the last 10 years is 0.187. ability distribution of X. List the possible values of x in ascending order. 8 correct: 0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Probability and Statistics Practice Problem**
**Problem Statement:**
According to an article, 39% of adults have experienced a breakup at least once during the last 10 years. Suppose 9 adults are randomly selected, and the number of adults who have experienced a breakup at least once during the last 10 years is recorded.
1. **Let X represent the number of adults who have experienced a breakup at least once during the last 10 years. Explain why X is a binomial random variable.**
X is a binomial random variable because:
- There are a fixed number of trials (n = 9), which refers to the 9 adults selected.
- Each trial has two possible outcomes: experiencing a breakup or not experiencing a breakup.
- The probability of experiencing a breakup (success) is constant (p = 0.39).
- The trials are independent, assuming that one adult’s experience does not influence another’s.
2. **Find the probability that at most one of the 9 adults experienced a breakup at least once during the last 10 years.**
To solve this, we need to find the sum of the probabilities for X = 0 and X = 1 using the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]
Where:
- \( n = 9 \)
- \( p = 0.39 \)
- \( k \) is the number of successes
Calculate \( P(X = 0) \) and \( P(X = 1) \).
3. **Find the probability that at least one of the 9 adults experienced a breakup at least once during the last 10 years.**
To find this, we need to determine:
\[
P(X \geq 1) = 1 - P(X = 0)
\]
Where \( P(X = 0) \) was found in the previous step.
4. **Complete the tables below to determine the probability distribution of X. List the possible values of X with their corresponding probabilities.**
- **Table 1:** Probability Distribution
| X | P(X = x) |
|---|----------|
| 0 | |
| 1 | |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4cf2595-fe80-4355-a077-fa7b5d3da7e9%2Fab0e2fb4-02b8-4b53-823f-e4a9f9a8f371%2Fd4g7afd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability and Statistics Practice Problem**
**Problem Statement:**
According to an article, 39% of adults have experienced a breakup at least once during the last 10 years. Suppose 9 adults are randomly selected, and the number of adults who have experienced a breakup at least once during the last 10 years is recorded.
1. **Let X represent the number of adults who have experienced a breakup at least once during the last 10 years. Explain why X is a binomial random variable.**
X is a binomial random variable because:
- There are a fixed number of trials (n = 9), which refers to the 9 adults selected.
- Each trial has two possible outcomes: experiencing a breakup or not experiencing a breakup.
- The probability of experiencing a breakup (success) is constant (p = 0.39).
- The trials are independent, assuming that one adult’s experience does not influence another’s.
2. **Find the probability that at most one of the 9 adults experienced a breakup at least once during the last 10 years.**
To solve this, we need to find the sum of the probabilities for X = 0 and X = 1 using the binomial probability formula:
\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]
Where:
- \( n = 9 \)
- \( p = 0.39 \)
- \( k \) is the number of successes
Calculate \( P(X = 0) \) and \( P(X = 1) \).
3. **Find the probability that at least one of the 9 adults experienced a breakup at least once during the last 10 years.**
To find this, we need to determine:
\[
P(X \geq 1) = 1 - P(X = 0)
\]
Where \( P(X = 0) \) was found in the previous step.
4. **Complete the tables below to determine the probability distribution of X. List the possible values of X with their corresponding probabilities.**
- **Table 1:** Probability Distribution
| X | P(X = x) |
|---|----------|
| 0 | |
| 1 | |
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