Customers using a self-service soda dispenser take an average of 12 ounces of soda with an SD of 4 ounces. Assume that the amount would be normally distributed. a. What is the chance that a randomly selected customer takes over 10 ounces of soda? b. What is the chance that a randomly selected customer takes between 13 and 14 ounces of soda? c. What is the chance that the next 100 customers will take an average of less than 12.24 ounces?
Answers
0.6915 is the chance that a randomly selected customer takes over 10 ounces of soda
Step-by-step explanation:
Customers using a self-service soda dispenser take an average of 12 ounces of soda with an SD of 4 ounces.
Mean = 12
SD = 4
10 ounces of soda
Z = ( Value - Mean)/SD
=> Z = (10 - 12)/4
=> Z = -2/4
=> Z = -0.5
Using Value of Z = 0.3085
Above 10 ounces = 1 - 0.3085 = 0.6915
0.6915 is the chance that a randomly selected customer takes over 10 ounces of soda
13 & 14
Z for 13 = ( 13 - 12)/4 = 0.25 0.5987
Z for 14 = (14 - 12)/4 = 0.5 0.6915
0.6915 - 0.5987 = 0.0928
0.0928 is chance that a randomly selected customer takes between 13 and 14 ounces of soda
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