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 0.38ounces.

A new 16-ounce cup that is being considered for use actually holds 16.7 ounces of drink.

ALREADY ANSWERED: Question 1. What is the probability that a new cup will overflow when filled by the automatic dispenser? (Use 4 decimal places)

ANSWER: .0327

Question 2. 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? (Use 2 decimal places in your answer and use 0.38 ounces for the standard deviation).

ounces.

Answer 1

1)

µ =    16                  
σ =    0.38                  
                      
P ( X ≥   16.70   ) = P( (X-µ)/σ ≥ (16.7-16) / 0.38)              
= P(Z ≥   1.842   ) = P( Z <   -1.842   ) =    0.0327   (answer)

2)

p = 0.006

z value at 0.006 = 2.512

Z=(X-µ)/σ

2.512 = (16.7 -µ) / 0.38

2.512*0.38 = 16.7 -µ

µ = 15.75

mean to be set at 15.75

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