Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. n USE SALT (a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) 15,87 (b) If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)? 26 x months
Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. n USE SALT (a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) 15,87 (b) If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)? 26 x months
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What is 12%
Transcribed Image Text:**Problem 20: Acrotime Watch Lifespan Analysis**
Acrotime is a manufacturer of quartz crystal watches. Acrotime researchers have determined that the watches have an average lifespan of **28 months** before certain electronic components begin to deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is **4 months**, and the distribution of lifetimes is normal.
**Questions:**
**(a)** If Acrotime guarantees a full refund on any defective watch for **2 years** (24 months) after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.)
- **Answer:** 15.87 %
**(b)** If Acrotime does not want to make refunds on more than **12%** of the watches it produces, how long should the guarantee period be (to the nearest month)?
- **Answer:** 26 months
**Guidance for Understanding:**
- Use statistical tools like Z-scores to determine the proportion of watches falling below a certain life expectancy.
- Utilize statistical tables or software to find percentages related to normal distribution.
- Modify guarantee periods based on desired refund rates and observed watch lifespan statistics.
**Interactive Help:**
- Buttons available for further understanding: "Read It," "Master It."
- Options to submit answers.
**Note:** This problem is designed to develop understanding of basic statistics concepts and their application in real-world scenarios such as manufacturing and quality assurance.
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