Jamaica Auto Service is a popular place for car service. It is also known that the mean time taken for Oervice at this station is 15 minutes per car and the standard deviation is 2.5 minutes. It is also known that the time taken for service on a car follows a normal distribution. a) What is the probability that a randomly selected customer will have to wait at most 14 minutes for service? (round to four decimal places) b) What percentage of customers will have to wait between 12 and 18 minutes for their service? (round to nearest percentage) c) Is it likely that it may take longer than 23 minutes for service? Find the likelihood of happening this and justify your answer.
Jamaica Auto Service is a popular place for car service. It is also known that the mean time taken for Oervice at this station is 15 minutes per car and the standard deviation is 2.5 minutes. It is also known that the time taken for service on a car follows a normal distribution. a) What is the probability that a randomly selected customer will have to wait at most 14 minutes for service? (round to four decimal places) b) What percentage of customers will have to wait between 12 and 18 minutes for their service? (round to nearest percentage) c) Is it likely that it may take longer than 23 minutes for service? Find the likelihood of happening this and justify your answer.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
![**Jamaica Auto Service Statistical Analysis**
Jamaica Auto Service is a popular place for car service. It is also known that the mean time taken for service at this station is 15 minutes per car and the standard deviation is 2.5 minutes. The time taken for service on a car follows a normal distribution.
**Questions:**
a) What is the probability that a randomly selected customer will have to wait at most 14 minutes for service? *(round to four decimal places)*
b) What percentage of customers will have to wait between 12 and 18 minutes for their service? *(round to nearest percentage)*
c) Is it likely that it may take longer than 23 minutes for service? Find the likelihood of this happening and justify your answer.
**Instructions:**
To solve these questions, you will need to use your knowledge of the properties of the normal distribution and perhaps a standard normal distribution table (Z-table).
Remember:
- To find probabilities related to the normal distribution, convert the given times to Z-scores using the formula:
\[ Z = \frac{(X - \mu)}{\sigma} \]
where \( \mu \) is the mean and \( \sigma \) is the standard deviation.
- Use the Z-scores to find corresponding probabilities from a Z-table.
**Example Calculation:**
If you want to find the probability that a randomly selected customer will have to wait less than or equal to 14 minutes, compute the Z-score for X = 14 minutes:
\[ Z = \frac{(14 - 15)}{2.5} = -0.4 \]
Look up -0.4 in the Z-table to find the cumulative probability.
We encourage you to try these calculations to enhance your statistical skills!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f54fed8-fa4e-41a3-be1d-05f34a1734d9%2Fdb8f9487-8f5f-4660-a9a4-d19e8f40ceaf%2F90sa5j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Jamaica Auto Service Statistical Analysis**
Jamaica Auto Service is a popular place for car service. It is also known that the mean time taken for service at this station is 15 minutes per car and the standard deviation is 2.5 minutes. The time taken for service on a car follows a normal distribution.
**Questions:**
a) What is the probability that a randomly selected customer will have to wait at most 14 minutes for service? *(round to four decimal places)*
b) What percentage of customers will have to wait between 12 and 18 minutes for their service? *(round to nearest percentage)*
c) Is it likely that it may take longer than 23 minutes for service? Find the likelihood of this happening and justify your answer.
**Instructions:**
To solve these questions, you will need to use your knowledge of the properties of the normal distribution and perhaps a standard normal distribution table (Z-table).
Remember:
- To find probabilities related to the normal distribution, convert the given times to Z-scores using the formula:
\[ Z = \frac{(X - \mu)}{\sigma} \]
where \( \mu \) is the mean and \( \sigma \) is the standard deviation.
- Use the Z-scores to find corresponding probabilities from a Z-table.
**Example Calculation:**
If you want to find the probability that a randomly selected customer will have to wait less than or equal to 14 minutes, compute the Z-score for X = 14 minutes:
\[ Z = \frac{(14 - 15)}{2.5} = -0.4 \]
Look up -0.4 in the Z-table to find the cumulative probability.
We encourage you to try these calculations to enhance your statistical skills!
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman