A mayor running for re-election claims that during his term, average municipal taxes have fallen by $100. A conscientious statistician wants to test this claim. He surveys 42 of his neighbors and finds that their taxes decreased (in dollars) as follows: 95, 117, 94, 108, 102, 102, 96, 85, 99, 113, 105, 93, 96, 110, 115, 98, 90, 109, 105, 82, 95, 79, 107, 114, 103, 95, 113, 86, 84, 105, 127, 101, 94, 108, 112, 104, 88, 97, 114, 93, 101, 109 The statistician assumes a population standard deviation of $10. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. 100 Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are normally distributed v o with distribution mean 100 o and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P(X = P(zv ) =

Jack's clothing sells on average, 25 shirts per week, sometimes a little more, sometimes a little less but typically a deviation of about 3. The cost per jacket is $65. Because Jack's is located in a sketchy part of town their insurance on inventory is 33% on all goods. The good news is free shipping to customers although UPS charges Jack's $8.50 for every delivery. It takes 2 weeks from the time jackets are ordered until they are received. Jack's supplier has said they only ship by pallet, and each pallet contains 75 jackets. If the reorder point is 50 what is the average flow time?

Please solve a, b, and c.  Note: Please explain and show steps for solutions especially for part c.

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