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A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.75 years. Assume the lifetime of a dishwasher is normally distributed. a) Identify the individual, variable, and type of variable in the context of this problem. The individual object is Select an answer The variable information collected from each individual is Select an answer This variable is a [Select an answer variable. b) What is the wording of the random variable X in the context of this problem? The random variable X - [Select an answer c) Why can the Empirical Rule be used to approximate probabilities on this problem? Select an answer d) Use the Empirical Rule to approximate the percentage of dishwashers that last between 10.25 years and 13.75 years. There is about % of dishwashers that last between 10.25 years and 13.75 years. e) If the warranty guarantees the dishwasher will last at least 10.25 years or your money back, what is the probability that the company will have to refund money to a customer? There is about % chance that the company will have to refund money to a customer.

A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.75 years. Assume the lifetime of a dishwasher is normally distributed. a) Identify the individual, variable, and type of variable in the context of this problem. The individual object is Select an answer The variable information collected from each individual is Select an answer This variable is a [Select an answer variable. b) What is the wording of the random variable X in the context of this problem? The random variable X - [Select an answer c) Why can the Empirical Rule be used to approximate probabilities on this problem? Select an answer d) Use the Empirical Rule to approximate the percentage of dishwashers that last between 10.25 years and 13.75 years. There is about % of dishwashers that last between 10.25 years and 13.75 years. e) If the warranty guarantees the dishwasher will last at least 10.25 years or your money back, what is the probability that the company will have to refund money to a customer? There is about % chance that the company will have to refund money to a customer.

MATLAB: An Introduction with Applications
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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### Problem Context: A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.75 years. Assume the lifetime of a dishwasher is normally distributed. ### Questions: **a) Identify the individual, variable, and type of variable in the context of this problem.** 1. **The individual object is:** - Options: (Dishwasher, Lifetime, Standard Deviation) 2. **The variable information collected from each individual is:** - Options: (Dishwasher, Lifetime, Standard Deviation) 3. **This variable is a:** - Options: (Qualitative, Quantitative) **b) What is the wording of the random variable X in the context of this problem?** 1. **The random variable X =** - Options: (Dishwasher, Lifetime, Standard Deviation) **c) Why can the Empirical Rule be used to approximate probabilities on this problem?** - Options for explanation: (Explain why the Empirical Rule applies to normally distributed data.) **d) Use the Empirical Rule to approximate the percentage of dishwashers that last between 10.25 years and 13.75 years.** - *Calculation:* - There is about **(options: %) of dishwashers that last between 10.25 years and 13.75 years. **e) If the warranty guarantees the dishwasher will last at least 10.25 years or your money back, what is the probability that the company will have to refund money to a customer?** - *Calculation:* - There is about **(options: %)** chance that the company will have to refund money to a customer. ### Explanation: **Graphs or Diagrams:** 1. **Normal Distribution Curve:** Imagine the normal distribution curve depicting the lifetime of dishwashers. The mean (average) lifetime is at the center (12 years), and the standard deviation (1.75 years) indicates the spread of the lifetimes around this mean. The Empirical Rule states that: - About 68% of the values lie within 1 standard deviation (10.25 to 13.75 years). - About 95% lie within 2 standard deviations. - About 99.7% lie within 3 standard deviations. These principles are used to approximate probabilities of dishwasher lifetimes within certain ranges.
Transcribed Image Text:### Problem Context: A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.75 years. Assume the lifetime of a dishwasher is normally distributed. ### Questions: **a) Identify the individual, variable, and type of variable in the context of this problem.** 1. **The individual object is:** - Options: (Dishwasher, Lifetime, Standard Deviation) 2. **The variable information collected from each individual is:** - Options: (Dishwasher, Lifetime, Standard Deviation) 3. **This variable is a:** - Options: (Qualitative, Quantitative) **b) What is the wording of the random variable X in the context of this problem?** 1. **The random variable X =** - Options: (Dishwasher, Lifetime, Standard Deviation) **c) Why can the Empirical Rule be used to approximate probabilities on this problem?** - Options for explanation: (Explain why the Empirical Rule applies to normally distributed data.) **d) Use the Empirical Rule to approximate the percentage of dishwashers that last between 10.25 years and 13.75 years.** - *Calculation:* - There is about **(options: %) of dishwashers that last between 10.25 years and 13.75 years. **e) If the warranty guarantees the dishwasher will last at least 10.25 years or your money back, what is the probability that the company will have to refund money to a customer?** - *Calculation:* - There is about **(options: %)** chance that the company will have to refund money to a customer. ### Explanation: **Graphs or Diagrams:** 1. **Normal Distribution Curve:** Imagine the normal distribution curve depicting the lifetime of dishwashers. The mean (average) lifetime is at the center (12 years), and the standard deviation (1.75 years) indicates the spread of the lifetimes around this mean. The Empirical Rule states that: - About 68% of the values lie within 1 standard deviation (10.25 to 13.75 years). - About 95% lie within 2 standard deviations. - About 99.7% lie within 3 standard deviations. These principles are used to approximate probabilities of dishwasher lifetimes within certain ranges.
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