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 ounce. A dr

Question 1108333: 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? Explain your reasoning.
Answer by UnlockStudyDocs(1) (Show Source): You can put this solution on YOUR website!

.
for normal distribution z score =(X-μ)/σ
a) probability that the drink is less than 11.6 fluid ounces
probability = P(X<11.6) = P(Z<-1)= 0.1587
b)
probability = P(11.4 c)
probability = P(X>12.2) = P(Z>2)= 1-P(Z<2)= 1-0.9772= 0.0228
as this probability is less than 0.05 level of unusual events; therefore this be considered an unusual event

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