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 0.2 fluid ounce. A drink is randomly selected. (a) Find the probability that the drink is less than 12 fluid ounces. (b) Find the probability that the drink is between 11.7 and 12 fluid ounces. (c) Find the probability that the drink is more than 12.5 fluid ounces. Can this be considered an unusual event? Explain your reasoning. (a) The probability that the drink is less than 12 fluid ounces is (Round to four decimal places as needed.)

Explanation / Answer

We take help of the Z tables to solve the questions. Params of the normal distribution have been given in the question and are stated below.

Mean = 12.2
Stdev = .2

We will standardize using the above params.

a. P(X<12) = P(Z< 12-12.2/.2) = P(Z<1) = 1-P(Z>1) = 1-.1587 = .8413

b. P(11.7<Z<12) = P( -2.5<Z<1) = .8413-.0062 = .8351

c. P(Z>12.5) = P(Z> 1.5) = 1-.9332 = .0668 This event would have been UNUSUAL if the probability was less than .05. Since it is more than .05 or the probability to be more than 12.5 fliud ounces is ,ore than 5% therefore the event is NOT unusual.

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