The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of 11.9 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 11.7 fluid ounces.
​(b) Find the probability that the drink is between 11.6 and 11.7 fluid ounces.
​(c) Find the probability that the drink is more than 12.2 fluid ounces. Can this be considered an unusual​ event? Explain your reasoning.
​(a) The probability that the drink is less than 11.7 fluid ounces is nothing.
​(Round to four decimal places as​ needed.)
​(b) The probability that the drink is between 11.6 and 11.7 fluid ounces is nothing.
​(Round to four decimal places as​ needed.)
​(c) The probability that the drink is more than 12.2 fluid ounces is nothing.
​(Round to four decimal places as​ needed.)
Is a drink containing more than 12.2 fluid ounces an unusual​ event? Choose the correct answer below.
A.
Yes​, because the probability that a drink contains more than 12.2 fluid ounces is less than ​0.05, this event is unusual.
B.
No​, because the probability that a drink contains more than 12.2 fluid ounces is less than ​0.05, this event is not unusual.
C.
No​, because the probability that a drink contains more than 12.2 fluid ounces is greater than ​0.05, this event is not unusual.
D.
Yes​, because the probability that a drink contains more than 12.2 fluid ounces is greater than ​0.05, this event is unusual.