The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown. t X P(X=x) 6 0.1 7 0.4 8 0.3 9 0.2 Complete parts (a) through (c) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. μ=(Type an integer or a decimal. Do not round.) o² = (Type an integer or a decimal. Do not round.) (b) Find the mean and the variance of the mean X for random samples of 49 cherry puffs. Px (Type an integer or a decimal. Do not round.) = (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 49 cherry puffs will be less than 7.9. The probability is (Round to four decimal places as needed.)
The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown. t X P(X=x) 6 0.1 7 0.4 8 0.3 9 0.2 Complete parts (a) through (c) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. μ=(Type an integer or a decimal. Do not round.) o² = (Type an integer or a decimal. Do not round.) (b) Find the mean and the variance of the mean X for random samples of 49 cherry puffs. Px (Type an integer or a decimal. Do not round.) = (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 49 cherry puffs will be less than 7.9. The probability is (Round to four decimal places as needed.)
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
- [Standard Normal Distribution Table - Page 2](#)
#### Exercises
1. **Parameter Calculation:**
a. Calculate the mean (\(\mu\)):
\[
\mu = \text{(Type an integer or a decimal. Do not round.)}
\]
b. Calculate the variance (\(\sigma^2\)):
\[
\sigma^2 = \text{(Type an integer or a decimal. Do not round.)}
\]
2. **Sample Mean and Variance:**
Determine the mean (\(\mu_{\bar{X}}\)) and the variance (\(\sigma^2_{\bar{X}}\)) of the mean (\(\bar{X}\)) for random samples of 49 cherry puffs:
\[
\mu_{\bar{X}} = \text{(Type an integer or a decimal. Do not round.)}
\]
\[
\sigma^2_{\bar{X}} = \text{(Round to three decimal places as needed.)}
\]
3. **Probability Calculation:**
Calculate the probability that the average number of cherries in 49 cherry puffs will be less than 7.9:
\[
\text{The probability is } \text{(Round to four decimal places as needed.)}
\]
#### Graphical Explanation
- **Probability Distribution Table**: The table above shows the number of cherries (x) and their corresponding probabilities (P(X=x)) in a cherry puff. For example, a cherry puff has a 0.1 probability of containing 6 cherries and a 0.4 probability of containing 7 cherries.
- **Visual Representation**: This distribution can be visualized using a bar graph where the x-axis represents the number of cherries,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7167d01a-fc0a-4c3f-ab49-29dc29956a80%2F37aed13b-1e69-47d3-9169-985b876d6481%2F7yezlq_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Probability Distribution of Cherries in a Cherry Puff
#### Probability Distribution
The random variable \( X \), representing the number of cherries in a cherry puff, has the probability distribution shown below:
| x | 6 | 7 | 8 | 9 |
|-----|-----|-----|-----|-----|
| P(X=x) | 0.1 | 0.4 | 0.3 | 0.2 |
You can refer to the standard normal distribution tables using the links below:
- [Standard Normal Distribution Table - Page 1](#)
- [Standard Normal Distribution Table - Page 2](#)
#### Exercises
1. **Parameter Calculation:**
a. Calculate the mean (\(\mu\)):
\[
\mu = \text{(Type an integer or a decimal. Do not round.)}
\]
b. Calculate the variance (\(\sigma^2\)):
\[
\sigma^2 = \text{(Type an integer or a decimal. Do not round.)}
\]
2. **Sample Mean and Variance:**
Determine the mean (\(\mu_{\bar{X}}\)) and the variance (\(\sigma^2_{\bar{X}}\)) of the mean (\(\bar{X}\)) for random samples of 49 cherry puffs:
\[
\mu_{\bar{X}} = \text{(Type an integer or a decimal. Do not round.)}
\]
\[
\sigma^2_{\bar{X}} = \text{(Round to three decimal places as needed.)}
\]
3. **Probability Calculation:**
Calculate the probability that the average number of cherries in 49 cherry puffs will be less than 7.9:
\[
\text{The probability is } \text{(Round to four decimal places as needed.)}
\]
#### Graphical Explanation
- **Probability Distribution Table**: The table above shows the number of cherries (x) and their corresponding probabilities (P(X=x)) in a cherry puff. For example, a cherry puff has a 0.1 probability of containing 6 cherries and a 0.4 probability of containing 7 cherries.
- **Visual Representation**: This distribution can be visualized using a bar graph where the x-axis represents the number of cherries,
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