Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost. Between 8 pounds and 11 pounds
+124 Well to make it as simple as possible we'll assume that distribution is one pound. So out values are 6, 7, 8, 9, 10, 11 and 12. A total of 7 possible amounts. Out of those 7, 4 of them are between 8 and 11(8, 9, 10 and 11). Therefore the probability of losing between 8 and 11 points is 4/7. This would change if your distribution was say 2 pounds, or half a pound.
+23251 Adonai is absolutely correct if you have a discrete distribution with weight losses of either 6 or 7 or 8 or ... 12 pounds.
He also correctly states that you need to alter your answer if the losses have a step of 2 pounds each, such as either 6 or 8 or 10 or 12, or 1/2 pound each, such as either 6 or 6 1/2 or 7 1/2 or ... or 12 pounds. And you solve these cases in exactly the way that he solved it for a step of 1 pound.
However, if you have a continuouts distribution, one that allows every possible loss (using every possible fraction) between 6 and 12 pounds, then find the distance between 6 and 12 pounds (12 - 6 = 6) and find the distance between 8 and 11 (11 - 8 = 3), then divide this sub-distance by the total distance: 3 / 6 = 1/2 = 0.50, giving a probability of 0.50.
