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 11.6 fluid ounces and a standard deviation of O.2 fluid ounce. A drink is randomly selected. (a) Find the probability that the drink is less than 11.5 fluid ounces. (b) Find the probability that the drink is between 11.2 and 11.5 fluid ounces (c) Find the probability that the drink is more than 12 fluid ounces. Can this be considered an unusual event? Explain your reasoning (a) The probability that the drink is less than 11.5 fluid ounces is (Round to four decimal places as needed.) (b) The probability that the drink is between 11.2 and 11.5 fluid ounces is (Round to four decimal places as needed.) (c) The probability that the drink is more than 12 fluid ounces is (Round to four decimal places as needed.) Is a drink containing more than 12 fluid ounces an unusual event? Choose the correct answer below d ounces s geater than O5 this ovent is nct unusual. O A. No, because the probability that a drink contains more than 12 flui O B. No, because the probability that a drink contains more than 12 fluid ounces is less than o lity that a drink contains more than 12 fluid ounces is greater than 0.05, this event is unusual t o drink containe more than 12 fliid nre ie locc than n n5 thie auont ic ini C. Yes, b Click to select your answer(s). Save for Later

Explanation / Answer

Solution(a)
Given in the question
Mean. = 11.6 and Standard deviation =0.2
We need to calculate P(Xbar<11.5)
Z = (11.5-11.6)/0.2 = -0.1/0.2 = -0.5
So from z table we found p-value
P(Xbar<11.5) = 0.3085
So there is 30.85% probability.
Solution(b)
P(11.2<Xbar<11.5) = P(Xbar<11.5)-P(Xbar<11.2)
Z = (11.2-11.6)/0.2 = -0.4/0.2 = -2
So from Z table
P(Xbar<11.2) = 0.0228
So P(11.2<Xbar<11.5) = 0.3085-0.0228 = 0.2857
So there is 28.57% probability.
Solution(c)
P(Xbar>12) = 1-P(Xbar<12)
Z = (12-11.6)/0.2 = 2
So from the z table we found
P(Xbar>12) = 1- 0.9772 = 0.0228
So there is 2.28% chances.

Its answer is D. yes, because the probabiltiy that a drink contains more than 12 fluid ounces is less than 0.05, the event is unusual.

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