Question: A manufacturer claims that the output voltage of a batch of shipped power supply units is normally distributed with a mean of \(9 \mathrm{~V}\) and standard deviation of \(0.3 \mathrm{~V}\). The upper and lower specifications for the voltage are \(8.95 \mathrm{~V}\) and \(9.05 \mathrm{~V}\).

1. What is the probability that a randomly chosen power supply unit fails to meet the specifications?
2. If we reject a randomly chosen power supply unit with a confidence of \(99 \%\) what is the Type error?
3. If we draw a sample of size 5 from the population, and \(\bar{X}\) denotes the sample mean
   (in Volts), then what probability distribution describes the random variable \(\bar{X} ?\)
   Does Central Limit Theorem apply?
4. If the real population mean of the batch is \(9.2 \mathrm{~V}-\) and \(\mathrm{not} 9 \mathrm{~V}\) as claimed- what is the Type II error in accepting the manufacturer's claim at \(95 \%\) confidence level? You may assume that the population standard deviation remains unchanged.

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