The Nelson Company makes the machines that automatically dispense soft drinks in

Question

The Nelson Company makes the machines that automatically dispense soft drinks into cups. Many national fast food chains such as McDonald's and Burger King use these machines. A study by the company shows that the actual volume of soft drink that goes into a 16-ounce cup per fill can be approximated by a normal model with mean 16 ounces and standard deviation 0.31 ounces. A new 16-ounce cup that is being considered for use actually holds 16.62 ounces of drink. a. What is the probability that a new cup will overflow when filled by the automatic dispenser? .0228 b. The company wishes to adjust the dispenser so that the probability that a new cup will overflow is .006. At what value should the mean amount dispensed by the machine be set to satisfy this wish? [ looking for help with this answer ] ounces. (Use 2 decimal places in your answer and use 0.31 ounces for the standard deviation).

Explanation / Answer

(a) Use mu = 16 and sigma = 0.31. The probability in terms of the z-score is P(x > 16.62) = P(z > (16.62 - 16)/0.31) = P(z > 2). Use a table (or calculator) to see that P(z > 2) = 1-P(z < 2) = 0.228 (b) To determine the probability that the overflow is 0.006 you need to find z0 such that 0.006 = P(z > z0) = 1-P(z

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