The shape of the distribution of the time required to get an oil change at a 20-minute oil-change facility is skewed right. However, records indicate that the mean time is 21.3 minutes, and the standard deviation is 3.1 minutes. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the required sample size below. A. The normal model cannot be used if the shape of the distribution is skewed right. B. The sample size needs to be less than 30. C. Any sample size could be used. D. The sample size needs to be greater than 30. (b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time less than 20 minutes? The probability is approximately . (Round to four decimal places as needed.)
The shape of the distribution of the time required to get an oil change at a 20-minute oil-change facility is skewed right. However, records indicate that the mean time is 21.3 minutes, and the standard deviation is 3.1 minutes. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the required sample size below. A. The normal model cannot be used if the shape of the distribution is skewed right. B. The sample size needs to be less than 30. C. Any sample size could be used. D. The sample size needs to be greater than 30. (b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time less than 20 minutes? The probability is approximately . (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
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![### Understanding Sampling and Probability in Skewed Distributions
The shape of the distribution of the time required to get an oil change at a 20-minute oil-change facility is skewed right. However, records indicate that the mean time is 21.3 minutes, and the standard deviation is 3.1 minutes. Consider the following questions and solutions:
**Click here to view the standard normal distribution table (page 1).**
**Click here to view the standard normal distribution table (page 2).**
---
#### (a) Determining Sample Size for Normal Model
To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
- Choose the required sample size below:
- A. The normal model cannot be used if the shape of the distribution is skewed right.
- B. The sample size needs to be less than 30.
- C. Any sample size could be used.
- **D. The sample size needs to be greater than 30.**
*(Correct Answer: D)*
The correct choice is **D**, indicating that the Central Limit Theorem suggests a sample size greater than 30 is sufficient for the normal model even if the original distribution is skewed.
#### (b) Calculating Probability
What is the probability that a random sample of \( n = 35 \) oil changes results in a sample mean time less than 20 minutes?
- The probability is approximately \[ \square \].
*(Round to four decimal places as needed.)*
---
This exercise highlights important considerations in using statistical models and distributions to predict outcomes based on sample data. Understanding sample size requirements and the influence of distribution shape is key for accurate statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8e90fb2-40f2-4192-8084-b4b52249ad4c%2F324c0795-2683-4bd1-ab04-64b592e7d709%2Fl389noi_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Sampling and Probability in Skewed Distributions
The shape of the distribution of the time required to get an oil change at a 20-minute oil-change facility is skewed right. However, records indicate that the mean time is 21.3 minutes, and the standard deviation is 3.1 minutes. Consider the following questions and solutions:
**Click here to view the standard normal distribution table (page 1).**
**Click here to view the standard normal distribution table (page 2).**
---
#### (a) Determining Sample Size for Normal Model
To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
- Choose the required sample size below:
- A. The normal model cannot be used if the shape of the distribution is skewed right.
- B. The sample size needs to be less than 30.
- C. Any sample size could be used.
- **D. The sample size needs to be greater than 30.**
*(Correct Answer: D)*
The correct choice is **D**, indicating that the Central Limit Theorem suggests a sample size greater than 30 is sufficient for the normal model even if the original distribution is skewed.
#### (b) Calculating Probability
What is the probability that a random sample of \( n = 35 \) oil changes results in a sample mean time less than 20 minutes?
- The probability is approximately \[ \square \].
*(Round to four decimal places as needed.)*
---
This exercise highlights important considerations in using statistical models and distributions to predict outcomes based on sample data. Understanding sample size requirements and the influence of distribution shape is key for accurate statistical analysis.
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