The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is skewed right. However, records indicate that the mean time is 11.2 minutes, and the standard deviation is 44 minutes Complete parts (a) through (c). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? O A. Any sample size could be used. O B. The sample size needs to be less than or equal to 30. C. The sample size needs to be greater than or equal to 30. O D. The normal model cannot be used if the shape of the distribution is skewed right. (b) What is the probability that a random sample of n= 45 oil changes results in a sample mean time less than 10 minutes? The probability is approximately 0.0337 (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager. There is a 10% chance of being at or below a mean oil-change time of minutes. (Round to one decimal place as needed.)
The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is skewed right. However, records indicate that the mean time is 11.2 minutes, and the standard deviation is 44 minutes Complete parts (a) through (c). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? O A. Any sample size could be used. O B. The sample size needs to be less than or equal to 30. C. The sample size needs to be greater than or equal to 30. O D. The normal model cannot be used if the shape of the distribution is skewed right. (b) What is the probability that a random sample of n= 45 oil changes results in a sample mean time less than 10 minutes? The probability is approximately 0.0337 (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager. There is a 10% chance of being at or below a mean oil-change time of minutes. (Round to one decimal place as needed.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Understanding Skewed Distribution in Oil-Change Time
The distribution of the time required to complete an oil change at a 10-minute oil-change facility is skewed to the right. Records indicate that the mean time is 11.2 minutes, with a standard deviation of 4.4 minutes.
#### Problem Analysis
**(a) Sample Size Requirement:**
To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
- Any sample size could be used.
- The sample size needs to be less than or equal to 30.
- **The sample size needs to be greater than or equal to 30.** *(Correct)*
- The normal model cannot be used if the shape of the distribution is skewed right.
**(b) Probability Calculation:**
What is the probability that a random sample of n = 45 oil changes results in a sample mean time less than 10 minutes?
- The probability is approximately **0.0337**. *(Rounded to four decimal places as needed)*
**(c) Setting Employee Goals:**
Suppose the manager offers a $50 bonus to each employee if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there is a 10% chance of the mean oil-change time being at or below which value? This will be the goal set by the manager.
- There is a 10% chance of being at or below a mean oil-change time of **[ ]** minutes. *(Round to one decimal place as needed)*
**Conclusion:**
Understanding the distribution and variability in oil-change times can help in setting realistic goals and improving efficiency in service delivery.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca98936e-33c7-4402-95ae-aeafe8e3f8b8%2F1358f893-1039-4caa-ab6b-db174db651cd%2F2ir6f3l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Skewed Distribution in Oil-Change Time
The distribution of the time required to complete an oil change at a 10-minute oil-change facility is skewed to the right. Records indicate that the mean time is 11.2 minutes, with a standard deviation of 4.4 minutes.
#### Problem Analysis
**(a) Sample Size Requirement:**
To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
- Any sample size could be used.
- The sample size needs to be less than or equal to 30.
- **The sample size needs to be greater than or equal to 30.** *(Correct)*
- The normal model cannot be used if the shape of the distribution is skewed right.
**(b) Probability Calculation:**
What is the probability that a random sample of n = 45 oil changes results in a sample mean time less than 10 minutes?
- The probability is approximately **0.0337**. *(Rounded to four decimal places as needed)*
**(c) Setting Employee Goals:**
Suppose the manager offers a $50 bonus to each employee if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there is a 10% chance of the mean oil-change time being at or below which value? This will be the goal set by the manager.
- There is a 10% chance of being at or below a mean oil-change time of **[ ]** minutes. *(Round to one decimal place as needed)*
**Conclusion:**
Understanding the distribution and variability in oil-change times can help in setting realistic goals and improving efficiency in service delivery.
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