SOLUTION: The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of 11.8 fluid ounces and a standard deviation of 0.2 fluid ounc

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Question 1118001: The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of 11.8 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected.
​(a) Find the probability that the drink is less than 11.6 fluid ounces.
​(b) Find the probability that the drink is between 11.4 and 11.6 fluid ounces.
​(c) Find the probability that the drink is more than 12.2 fluid ounces. Can this be considered an unusual​ event?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd
For a. (11.6-11.8)/0.2 is a z<-1 a probability 0.1587
For b it is z between -1 and -2. This probability is 0.1359
For c it is z greater than 2 which has probability of 0.0228. This may be considered an unusual event depending upon what criteria/probability one chooses to call unusual.