19. The life of a Immobilize Breeze blower is normally distributed with &ere; population mean 48 months and population standard deviation 14 months. The manufacturer will replace some fan that wears out during the guarantee period: a) What percentage of fans will have to be replaced if the guarantee period is 36 months? (resolution to 2 decimal places) ANS b)_ What should the guarantee period be if the manufacturer does non want to replace more than 5% of the fans? (answer to the closest month) Ans_
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Answer
The length of the biography of a positive type of refrigerator is approximately normally unfocused with a mean of 4.8 eld and a standard deviation of 1.3 years. a. If this machine is guaranteed for 2 years, what is the probability that the simple machine you purchased will need replacement under the guarantee? b. What period of time should the manufacturer give arsenic a guarantee if it is willing to replace only $0.5 \%$ of the machines?
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therein problem, we're told that the life of a refrigerator is normally distributed with a meanspirited of 4.8 geezerhood and the standard divagation of 1.3 years. And in part they were asked if the machine is guaranteed for deuce years. What is the probability that you would have to replace it subordinate warranty if you bought it so it's replaced under warranty? If IT lasts for inferior than two years? We're looking for the probability that X sprightliness of the machine is less than two and using the said conversion if that is Fairness X minus mu over Sigma. So this is equal to the probability that same is less than to negative 4.8 over 1.3, and that comes out to 0.156 So the probability of replacement it under warranty if you buy information technology is 0.156 on a part B were asked what metre the manufacturing business should give Eastern Samoa the guarantee if they lone want replace 0.5%. So let's say the guaranty is que years, so if if the prison term that the machine last is lesson K years they replaced IT under warranty, and they want the chance that occurring to be half a percent. So that's the probability that the life is little than K years is capable zero point 005 That's half a percent. So we can also view this as the probability that Ezed is fewer than K subtraction 4.8. Over 1.3 equals nothing point 005 And using either the acceptable normal tables or a calculator surgery computer software, you can find that the correspondent corresponding Zed score is disadvantageous two point 576 which implies that K is equal to one point 451 days. And so you want to set the warranty at 1.451 years if you solitary want to replace incomplete a percent of them.
The Life of a Freeze Breeze Electric Fan
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