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# Model Ratio Percentage

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1) What percentage of this model radio will last longer than 9.5 years?

2) Suppose the manufacturer guarantees the radio for 8 years. What percentage of radios will have to be replaced?

3) Suppose the manufacturer is willing to replace only 2% of this model radio. What should be the length of the guarantee?

##### Solution Summary

The percentage of this model radio will last longer than 9.5 years are determined. The manufacturer guarantees the radio for 8 years. What percentage of radios will have to be replaced are analyzed.

##### Solution Preview

Category: Statistics
Subject: Central Limit Theorem
Details: A radio manufacturer believes that the length of life, x (in years), of its ZZZZ model radio is approximately normally distributed with mean 12 and standard deviation 2.5

Please show the work with the ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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