The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown. 5 | 0.4 X P(X=x) 4 0.2 6 0.3 7 0.1 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
The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown. 5 | 0.4 X P(X=x) 4 0.2 6 0.3 7 0.1 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
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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solve the following
[Click here to view page 2 of the standard normal distribution table.](#)
(a) **Find the mean μ and the variance σ² of X.**
- \(\mu\) = \( \square \)
(Type an integer or a decimal. Do not round.)
- \(\sigma^2\) = \( \square \)
(Type an integer or a decimal. Do not round.)
(b) **Find the mean \( \mu_{\bar{X}}\) and the variance \( \sigma^2_{\bar{X}} \) of the mean \( \bar{X} \) for random samples of 49 cherry puffs.**
- \(\mu_{\bar{X}}\) = \( \square \)
(Type an integer or a decimal. Do not round.)
- \(\sigma^2_{\bar{X}}\) = \( \square \)
(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 5.5.**
- The probability is \( \square \).
(Round to four decimal places as needed.)
### Explanation of Graphs and Tables
The table provided is a probability distribution table for the random variable \(X\). It lists the possible values that \(X\) can take (4, 5, 6, 7) along with their corresponding probabilities (0.2, 0.4, 0.3, 0.1). This information is essential for performing calculations related to the mean, variance, and probabilities associated with \(X\).
Please fill in the blanks with appropriate calculations based on the provided data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b4ff4f7-2c8f-41ef-8afc-ff3d6486dbd5%2Fc95824dc-bb73-4ec6-b40d-1bb0316407d0%2Fqefcwje_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Distribution of Cherries in Cherry Puffs
The random variable \(X\), representing the number of cherries in a cherry puff, has the probability distribution shown in the table.
| \(x\) | 4 | 5 | 6 | 7 |
|------|---|---|---|---|
| \(P(X = x)\) | 0.2 | 0.4 | 0.3 | 0.1 |
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.](#)
(a) **Find the mean μ and the variance σ² of X.**
- \(\mu\) = \( \square \)
(Type an integer or a decimal. Do not round.)
- \(\sigma^2\) = \( \square \)
(Type an integer or a decimal. Do not round.)
(b) **Find the mean \( \mu_{\bar{X}}\) and the variance \( \sigma^2_{\bar{X}} \) of the mean \( \bar{X} \) for random samples of 49 cherry puffs.**
- \(\mu_{\bar{X}}\) = \( \square \)
(Type an integer or a decimal. Do not round.)
- \(\sigma^2_{\bar{X}}\) = \( \square \)
(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 5.5.**
- The probability is \( \square \).
(Round to four decimal places as needed.)
### Explanation of Graphs and Tables
The table provided is a probability distribution table for the random variable \(X\). It lists the possible values that \(X\) can take (4, 5, 6, 7) along with their corresponding probabilities (0.2, 0.4, 0.3, 0.1). This information is essential for performing calculations related to the mean, variance, and probabilities associated with \(X\).
Please fill in the blanks with appropriate calculations based on the provided data.
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