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Probability: fax costs

Please help me with the attached questions. Please also provide the formulas used and how the numbers are plugged into the formula. Thank you.

1.) Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.

(a) At the .01 level of significance, is the true mean greater than 10?
(b) Use Excel to find the right-tail p-value.

2) A coin was flipped 60 times and came up heads 38 times.

(a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations.
(b) Calculate a p-value and interpret it.

3) The Web-based company Oh Baby! Gifts have a goal of processing 95 percent of its orders on the same day they are received.

If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .025?

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The solution explains the concepts of probability using examples.

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