Assume that the weight loss for the first two months of a diet program has a uniform distribution over the interval 6 to 12 pounds. Find the probability that a person on this diet loses between 9 and 12 pounds in the first two months.
a. 1/4 b. 1/2 c. 1/3 d. 2/3
9 to 12 is half of the full interval. Since the distribution is uniform, the probability is 1/2
I am surprised there are no zeros or weight gains.
To find the probability that a person on this diet loses between 9 and 12 pounds in the first two months, we first need to find the total range of weight loss for the first two months.
Given that the weight loss has a uniform distribution over the interval 6 to 12 pounds, the range of weight loss is 12 - 6 = 6 pounds.
Next, we need to find the probability of losing between 9 and 12 pounds. To do that, we need to find the proportion of the total range that corresponds to this range.
The range of 9 to 12 pounds is 12 - 9 = 3 pounds.
Thus, the probability of losing between 9 and 12 pounds is 3 / 6 = 1 / 2.
Therefore, the answer is option b. 1/2.