# How many ounces are in a scoop of ice cream

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Ice cream usually comes in 1.5 quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some variability in the amount of ice cream in a box as well as the amount of ice cream scooped out. We represent the amount of ice cream in the box as X and the amount scooped out as Y. Suppose these random variables have the following means, standard deviations, and variances. Mean SDVariance 48 0.25 0.0625 (a) An entire box of ice cream, plus 6 scoops from a second box is served at a party. How much ice cream do you expect to have been served at this party? fluid ounces 60 What is the standard deviation of the amount of ice cream served? (Round your answer to two decimal places.) 1.03 Xfluid ounces Enter a number (b) How much ice cream would you expect to be left in the box after scooping out one scoop of ice cream? That is, find the expected value of X - Y. fluid ounces What is the standard deviation of the amount left in the box? (Round your answer to two decimal places.) fluid ounces (c) Using the context of this exercise, explain why we add variances when we subtract one random variable from another Initially we do not know exactly how much ice cream is in the box, then we scoop out an unknown amount. Because we removed an unknown amount from a box where the amount of ice cream was unknown, we must add the variances to be confident of the difference when we subtract one unknown random variable from another unknown random variable Initially we do not know exactly how much ice cream is in the box, then we scoop out a known amount. Because we removed a known amount from a box where the amount of ice cream was unknown, we must add the variances to be confident of the difference when we subtract one known random variable from another unknown random variable. Initially we know exactly how much ice cream is in the box, then we scoop out an unknown amount. Because we removed an unknown amount, we must add the variances to be confident of the difference when we subtract one unknown random variable from another known random variable Initially we do know exactly how much ice cream is in the box, then we scoop out a known amount. Because we removed a known amount from a box where the amount of ice cream was known, we must add the variances to be confident of the difference when we subtract one known random variable from another known random variable