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**YOU ARE REQUIRED TO SHOW WORK FOR THIS QUESTION TO RECEIVE CREDIT!** A bottled beverage company claims that the average amount of liquid in its 16-oz bottles is 16.0 ounces, with a standard deviation of 0.4 ounces. A quality control inspector selects a random sample of 90 bottles from the production line. (Round to 3 decimal places as needed)   Find the probability that the sample mean amount is greater than 16.1 ounces. [a]

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**YOU ARE REQUIRED TO SHOW WORK FOR THIS QUESTION TO RECEIVE CREDIT!** A coffee shop reports that the average wait time for customers to receive their drinks during morning hours is [a] minutes, with a standard deviation of [b] minutes. A random sample of [c] customers is selected. (Round to 3 decimal places as needed)   Calculate the standard deviation of the sample mean (aka the standard error). 

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**YOU ARE REQUIRED TO SHOW WORK FOR THIS QUESTION TO RECEIVE CREDIT!** Bob is picking what sport he wants to play this school year. The probability that he plays soccer is 0.18, the probability that he plays baseball is 0.34, and the probability that he plays both soccer and baseball is 0.15. (Round to three decimal places as needed.)   a. What is the probability that Bob plays soccer or baseball? [a] b. What is the probability that Bob does not play baseball but plays soccer? [b] c. Based off your answer for part b, would it be unusual for Bob to play baseball but not soccer? [c] (yes/no), because the probability is [d] (less than/more than) 0.05. d. If we know that Bob plays baseball, what is the probability that Bob also plays soccer? [e]

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**YOU ARE REQUIRED TO SHOW WORK FOR THIS QUESTION TO RECEIVE CREDIT!** The following table summarizes data from a sample of office employees. They were asked whether they work remotely and whether they prefer flexible work hours. Prefer flexible work hours Does not prefer flexible work hours Work remotely [a] [c] Does not work remotely [b] [d] (Round to three decimal places as needed.)   Find the probability that a randomly selected employee works remotely given we know they prefer flexible work hours.