The amounts a soft drink machine is designed to dispense for each drink are norm

Question

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 11.8 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. (a) The probability that the drink is less than 12.1 fluid ounces is (Round to four decimal places as needed.) (b) The probability that the drink is between 11.8 and 12.1 fluid ounces is (Round to four decimal places as needed.) (c) The probability that the drink is more than 12.7 fluid ounces is (Round to four decimal places as needed.) Is a drink containing more than 12.7 fluid ounces an unusual event? Choose the correct answer below. A. No. because the probability that a drink contains more than 12.7 fluid ounces is greater than 0.05. this event is not unusual. B. Yes. because the probability that a drink contains more than 12.7 fluid ounces is greater than 0.05, this event is unusual. C. No. because the probability that a drink contains more than 12.7 fluid ounces is less than 0.05. this event is not unusual. D. Yes. because the probability that a drink contains more than 12.7 fluid ounces is less than 0.05, this event is unusual.

Explanation / Answer

as from normal distribution z=(X-mean)/std deviation

a)P(X<12.1)=P(Z<(12.1-12.2)/0.3)=P(Z<-0.3333)=0.3694

b)P(11.8<X<12.1)=P(-1.3333<Z<-0.3333)=0.3694-0.0912=0.2782

c)P(X>12.7)=1-P(X<12.7)=1-P(Z,1.6667)=1-0.9522=0.0478

option D is correct

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