[Solution] The amount (unit: ounce) of fill dispensed by a bottle machine is normally distributed with mean at μ and variance as σ^2. A sample
Question: The amount (unit: ounce) of fill dispensed by a bottle machine is normally distributed with mean at \(\mu\) and variance as \(\sigma^{2}\). A sample of size \(n(n=16)\) filled bottles is randomly selected, and the amount of fill is measured for each bottle. It is assumed that under normal production condition, \(\mu=30\) and \(\sigma^{2}=9\).
- What is the distribution of sample mean \(\bar{X}\) ?
- In order to control the quality, fill amounts in bottles are compared with two boundaries, \(b_{1}\) and \(b_{2}\), which are symmetric about \(\mu\). How can we define the boundaries such that \(P\left(\bar{X} \leq b_{1}\right.\) or \(\bar{X}\ge {{b}_{2}})=0.00270\) ?
Deliverable: Word Document 
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