Question 1105140: 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 fluid ounces.
(b) Find the probability that the drink is between 11.8 and 12 fluid ounces.
(c) Find the probability that the drink is more than 12.6 fluid ounces. Can this be considered an unusual event
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! using z=(x-mean)/sd
for 12, z=(12-12.2)/0.3, so want z <-2/3
probability is 0.2525
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between 11.8 and 12
need 11.8, which is a z of -4/3
want z between -4/3 and -2/3
probability is 0.1613
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More than 12.6 ounces is a z > +4/3, which is 0.0912. This would not generally be considered unusual unless one decided anything above the 90th percentile was.
z on calculator 2nd VARS 2 and the z values -6, -2/3 (I use -6 but anything less is fine). This could be done from the table as well.
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