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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 12-oz bottles is 12.0 ounces, with a standard deviation of 0.3 ounces. A quality control inspector selects a random sample of 60 bottles from the production line. (Round to 3 decimal places as needed) Find the probability that the sample mean amount is less than 12.05 ounces. [a]
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**YOU ARE REQUIRED TO SHOW WORK FOR THIS QUESTION TO RECEIVE CREDIT!** The battery life of a certain brand of wireless headphones is normally distributed, with a mean of 45.5 hours and a standard deviation of 4.1 hours. (Round to 3 decimal places as needed.) a. Find the probability that a randomly selected pair of headphones has a battery life of less than 37 hours. [a] b. Find the battery life that represents the 19th percentile. [b] c. Find the two battery life values that represent the middle 44% of all battery lives. (Put the smaller value first.) [c], [d]
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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!** The following is a probability distribution table for a discrete random variable, X. x P(X = x) [a] 0.43 [b] 0.12 [c] 0.27 [d] 0.18 Calculate the mean value of X.
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The following is a probability distribution table for a discrete random variable, X. x P(X = x) 20 [a] 35 0.31 40 0.25 55 0.07 a. Fill in the missing probability in the table, P(X = 20) b. Calculate the probability that X is more than 35. [b]
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