Question

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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 11.8 fluid Ounces. (b) Find the probability that the drink is between 11.6 and 11.8 fluid Ounces. (c) Find the probability that the drink is more than 12.4 fluid Ounces. Can this be considered an unusual event? Explain your reasoning (a) The probability that the drink is less than 11.8 fluid ounces is (Round to four decimal places as needed) (b) The probability that the drink is between 116 and 11.8 fluid ounces is (Round to four decimal places as needed) (c) The probability that the drink is more than 12 4 fluid ounces is (Round to four decimal places as needed Is a drink containing more than 124 fluid Ounces an unusual event? Choose the correct answer below OA. Yes, because the probability that a drink contains more than 124 fluid Ounces is greater than 0 05, this event is unusual OB. No, because the probability that a drink contains more than 12,4 fluid Ounces is greater than 0 05 this event is not unusual O C. No, because the probability that a drink contains more than 124 fluid Ounces is less than 0.05, this event is not unusual OD. Yes, because the probability that a drink contains more than 12.4 fluid Ounces is less than 0.05, this event is unusual.

Answer 1

Answers:

a. Probability that the drink is less than 11.8 fluid ounces is 0.3085

b. The probability that the drink is between 11.6 and 11.8 fluid ounces is 0.2417

c. Probability that the drink is more than 12.4 fluid ounces is 0.0062

Is drink containing more than 12.4 fluid ounces is an unusual event? Yes, because the probability that a drink contains more than 12.4 fluid ounces is less than 0.05, this event is unusual.

Complete solution is given in attached images:

let soft-drink X= Amount of of drink machine dispense Given xou N (11.9, (0-233) a) Probability less that fluid the drink is ounces than 11.8 p (x< 11.8) 14-11-9 P 1.8-Hog < 0:2 p (22-0.5) Z Nro, il = 0.3085 b) The probability probability that & fluid the drink is between ounices is 11.6 11.8 - Z Z < O- 2 = p (11.6 < x <11.8) P ( 11.6-11.9 T1:8-11.9 7-15C22-0.5 Ć PZL-005) P (2 2-15) 0 0.0668 0.2417 17 p. ZNO,) -0.3085 1

mone c) The probability that than 12.4 fluid the drink is. ounces is 1204–11.9 P (x212.4) P X-11.9 0.2 > o. 2 Piero ZNMON P(Z > 2.5) =o0062 more an. event, Drink_containing is unusual probability 12.4 fluid ounces this ps is that than 12044_Fluid Ounces because the drink. contains more than is less than 0.05, unsusual. event

Thank You.