The amounts a soft drink machine is designed to dispense for

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.3 fluid ounces and a standard deviation of 03 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 fuid ounces. (c) Find the probability that the drink is more than 12.8 fluid ounces. Can this be considered an unusual event? Explain your reasoning (a) The probability that the drink is less than 12.1 fuid ounces is (Round to four decimal places as needed.) (b) The probability that the drink is between 11.8 and 12.1 fuid ounces is (Round to four decimal places as needed.) (c) The probability that the drink is more than 12.8 fuid ounces is (Round to four decimal places as needed.) ls a drink containing more than 12.8fluid ounces an unusual event? Choose the correct answer below. O A. Yes, because the probability that a drink contains more than 12.8 fuid ounces is less than 0.05, this event is unusual. O B. No, because the probability that a drink contains more than 12.8 fuid ounces is less than 0.05, this eventis not unusual O C. Yes, because the probability that a drink contains more than 12.8 fuid ounces is greater than 0.05.this event is unusual. O D. No, because the probability that a drink contains more than 12 8 fuid ounces is greater than 0.05. this event is not unusual

Solution

mean = u = 12.3

SD = 0.3

a) Less than 12.1 :

z = (x - u) / SD
z = (12.1 - 12.3) / 0.3
z = -0.6666666666666666666666666666666666666666666666666667

P(z < -0.6666666666666666666666666666666666666666666666666667) can be found using this link :

https://www.easycalculation.com/statistics/p-value-for-z-score.php

P(z < -0.6666666666666666666666666666666666666666666666666667) = .2525

0.2525 ---> ANSWER to a

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b) Between 11.8 and 12.1 :

z = (x - u) / SD
z = (11.8 - 12.3) / 0.3
z = -1.6666666666666667

P(z < -1.6666666666666667) = 0.0478

So, P(-1.67 < z < -0.67) = 0.2525 - 0.0478 ----> 0.2047

0.2047 --> ANSWER to b

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c) More than 12.8 :

z = (x - u) / SD

z = (12.8 - 12.3) / 0.3

z = 1.6666666666666667

P(z > 1.6666666666666667) = 0.0478

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d) z = (12.8 - 12.3) / 0.3 = 0.5/0.3 = 5/3 = 1.666666666667

From the above part, we found that P(x > 12.8) = 0.0478, i.e approx 0.05, which is almost 1 in 20, which is indeed unusual

So, option A --> ANSWER