Question 1045256: The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.2 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.
(a) Find the probability that the drink is less than 12.1 fluid ounces.
(b) Find the probability that the drink is between 12 and 12.1 fluid ounces.
(c) Find the probability that the drink is more than 12.7 fluid ounces. Can this be considered an unusual event? Explain your reasoning.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
for 12.1
z=(12.1-12.2)/0.3=-(1/3)
Probability z < -1/3 is 0.3694.
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probability z is less than 12 is z=(12-12.2)0.3=-(0.2)/(0.3)
z<-2/3 is 0.2525.
The probability z is between -1/3 and -2/3, or the drinks between 12.0 and 12.1 ounces is 0.1169, the difference between their probabilities. The first is -oo to -1/3, the second from -oo to -2/3, and that difference has to be the probability between -1/3 and -2/3,
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z=(12.7-12.2)=+1.67 or +(5/3)
z=0.0478
It would happen by chance 1 out of 21 times. If you said it could not happen by chance more than 1 time out of 20 then this would be acceptable. If you said it could not happen by chance more than 1 time out of 30, then this is not acceptable. You have to define the level before you do the study, and not draw conclusions based on what you think after you see the results. An unusual event? It depends upon what was defined as unusual. Typically, <5% is used, but this number was picked out of the air by Sir Ronald Fisher, and is not immutable.
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