a) Find the mean μ and the variance o² of X. (Type an integer or a decimal. Do not round.) ²=(Type an integer or a decimal. Do not round.) b) Find the mean µ and the variance of the mean X for random samples of 64 cherry puffs ¹x (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 64 cherry puffs will be less than 5.6.
a) Find the mean μ and the variance o² of X. (Type an integer or a decimal. Do not round.) ²=(Type an integer or a decimal. Do not round.) b) Find the mean µ and the variance of the mean X for random samples of 64 cherry puffs ¹x (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 64 cherry puffs will be less than 5.6.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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solve the following
- [Click here to view page 2 of the standard normal distribution table.](#)
Complete parts (a) through (c) below:
#### (a) Find the mean \( \mu \) and the variance \( \sigma^2 \) of \( X \).
\[ \mu = \text{(Type an integer or a decimal. Do not round.)} \]
\[ \sigma^2 = \text{(Type an integer or a decimal. Do not round.)} \]
#### (b) Find the mean \( \mu_{\bar{X}} \) and the variance \( \sigma^2_{\bar{X}} \) of the mean \( \bar{X} \) for random samples of 64 cherry puffs.
\[ \mu_{\bar{X}} = \text{(Type an integer or a decimal. Do not round.)} \]
\[ \sigma^2_{\bar{X}} = \text{(Round to three decimal places as needed.)} \]
#### (c) Find the probability that the average number of cherries in 64 cherry puffs will be less than 5.6.
\[ \text{The probability is } \_\_\_ \]
(Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d1e5150-1781-42a0-9e07-3d8cfcc0113b%2Fa8f9d4c7-a55c-4153-bf81-5bd1194e2ff8%2Feoa4jfm_processed.png&w=3840&q=75)
Transcribed Image Text:### Distribution of Cherries in Cherry Puffs
The random variable \( X \), representing the number of cherries in a cherry puff, has the probability distribution shown below:
| \( x \) | 4 | 5 | 6 | 7 |
|----------------|-----|-----|-----|-----|
| \( P(X = x) \) | 0.2 | 0.4 | 0.3 | 0.1 |
You can access the standard normal distribution tables through the following links:
- [Click here to view page 1 of the standard normal distribution table.](#)
- [Click here to view page 2 of the standard normal distribution table.](#)
Complete parts (a) through (c) below:
#### (a) Find the mean \( \mu \) and the variance \( \sigma^2 \) of \( X \).
\[ \mu = \text{(Type an integer or a decimal. Do not round.)} \]
\[ \sigma^2 = \text{(Type an integer or a decimal. Do not round.)} \]
#### (b) Find the mean \( \mu_{\bar{X}} \) and the variance \( \sigma^2_{\bar{X}} \) of the mean \( \bar{X} \) for random samples of 64 cherry puffs.
\[ \mu_{\bar{X}} = \text{(Type an integer or a decimal. Do not round.)} \]
\[ \sigma^2_{\bar{X}} = \text{(Round to three decimal places as needed.)} \]
#### (c) Find the probability that the average number of cherries in 64 cherry puffs will be less than 5.6.
\[ \text{The probability is } \_\_\_ \]
(Round to four decimal places as needed.)
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