The amount of hot chocolate dispensed by a hot chocolate machine is normally distributed with a mean of 16.0 oz. and a standard deviation of 2 oz. If the cups hold 18.0 oz., what is the probability that a selected cup will be overfilled?

Probability that a selected cup will be overfilled is 0.15866 .

Step-by-step explanation:

We are given that the amount of hot chocolate dispensed by a hot chocolate machine is normally distributed with a mean of 16.0 oz. and a standard deviation of 2 oz.

Let X = Amount of hot chocolate dispensed by a hot chocolate machine, so X ~ N()

The standard normal z distribution is given by;

              Z = ~ N(0,1)

We are also given that the cups hold 18.0 oz.

Now, probability that a selected cup will be overfilled = P(X > 18.0 oz)

P(X > 18.0) = P( >  ) = P(Z > 1) = 1 - P(Z <= 1)

                                               = 1 - 0.84134= 0.15866

Therefore, the probability that a selected cup will be overfilled is 0.15866.

answer: slight chance that it will happen

step-by-step explanation: