The average number of moves a person makes in his or her lifetime is 12 and the standard deviation is 3.3. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answers to four decimal places and intermediate z value calculations to two decimal place Part 1 of 3 Find the probability that the mean of a sample of 25 people is less than 10. P(X<10)= Part 2 of 3 X Part 3 of 3 Find the probability that the mean of a sample of 25 people is greater than 10. P(X>10)- X S X S Find the probability that the mean of a sample of 25 people is between 11 and 12. P(11
The average number of moves a person makes in his or her lifetime is 12 and the standard deviation is 3.3. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answers to four decimal places and intermediate z value calculations to two decimal place Part 1 of 3 Find the probability that the mean of a sample of 25 people is less than 10. P(X<10)= Part 2 of 3 X Part 3 of 3 Find the probability that the mean of a sample of 25 people is greater than 10. P(X>10)- X S X S Find the probability that the mean of a sample of 25 people is between 11 and 12. P(11
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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![The problem presented involves calculating probabilities related to the mean number of moves a person makes in their lifetime, using statistical concepts. Here's a detailed transcription suitable for an educational website:
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### Statistical Probability and Sample Means
The average number of moves a person makes in his or her lifetime is 12, with a standard deviation of 3.3. This scenario assumes the sample is taken from a large population, and the correction factor can be ignored. Final answers should be rounded to four decimal places, and intermediate z value calculations should be rounded to two decimal places.
#### Part 1 of 3
**Objective:** Find the probability that the mean of a sample of 25 people is less than 10.
\[ P(\overline{X} < 10) = \boxed{\phantom{5}} \]
---
#### Part 2 of 3
**Objective:** Find the probability that the mean of a sample of 25 people is greater than 10.
\[ P(\overline{X} > 10) = \boxed{\phantom{5}} \]
---
#### Part 3 of 3
**Objective:** Find the probability that the mean of a sample of 25 people is between 11 and 12.
\[ P(11 < \overline{X} < 12) = \boxed{\phantom{5}} \]
---
### Explanation:
These tasks involve the use of the normal distribution and the concept of the sampling distribution of the sample mean. With a known sample size (\(n = 25\)), the mean (\(\mu = 12\)), and the standard deviation (\(\sigma = 3.3\)), you can calculate the standard error and use the z-score formula to find the probabilities:
1. **Calculate the standard error (SE):**
\[
SE = \frac{\sigma}{\sqrt{n}}
\]
2. **Use the z-score formula:**
\[
z = \frac{\overline{X} - \mu}{SE}
\]
These calculations lead to the probabilities based on the z-scores from the standard normal distribution tables.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2743f58a-999a-485c-8435-d316e3b49890%2F7c0d8c64-76bf-4a00-ac4d-6cbe67e3fe71%2Fewg5oh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem presented involves calculating probabilities related to the mean number of moves a person makes in their lifetime, using statistical concepts. Here's a detailed transcription suitable for an educational website:
---
### Statistical Probability and Sample Means
The average number of moves a person makes in his or her lifetime is 12, with a standard deviation of 3.3. This scenario assumes the sample is taken from a large population, and the correction factor can be ignored. Final answers should be rounded to four decimal places, and intermediate z value calculations should be rounded to two decimal places.
#### Part 1 of 3
**Objective:** Find the probability that the mean of a sample of 25 people is less than 10.
\[ P(\overline{X} < 10) = \boxed{\phantom{5}} \]
---
#### Part 2 of 3
**Objective:** Find the probability that the mean of a sample of 25 people is greater than 10.
\[ P(\overline{X} > 10) = \boxed{\phantom{5}} \]
---
#### Part 3 of 3
**Objective:** Find the probability that the mean of a sample of 25 people is between 11 and 12.
\[ P(11 < \overline{X} < 12) = \boxed{\phantom{5}} \]
---
### Explanation:
These tasks involve the use of the normal distribution and the concept of the sampling distribution of the sample mean. With a known sample size (\(n = 25\)), the mean (\(\mu = 12\)), and the standard deviation (\(\sigma = 3.3\)), you can calculate the standard error and use the z-score formula to find the probabilities:
1. **Calculate the standard error (SE):**
\[
SE = \frac{\sigma}{\sqrt{n}}
\]
2. **Use the z-score formula:**
\[
z = \frac{\overline{X} - \mu}{SE}
\]
These calculations lead to the probabilities based on the z-scores from the standard normal distribution tables.
---
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