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 10.5 and 12 pounds in the first two months.

To find the probability that a person on this diet loses between 10.5 and 12 pounds in the first two months, we can use the properties of a uniform distribution.

A uniform distribution is a continuous probability distribution where all values within a certain interval are equally likely to occur. In this case, the weight loss is uniformly distributed over the interval 6 to 12 pounds.

To calculate the probability, we need to find the relative length of the interval between 10.5 and 12 pounds compared to the total length of the interval from 6 to 12 pounds.

Total length of the interval from 6 to 12 pounds:
12 - 6 = 6 pounds

Length of the interval between 10.5 and 12 pounds:
12 - 10.5 = 1.5 pounds

Now, we can calculate the probability by dividing the length of the interval between 10.5 and 12 pounds by the total length of the interval:

Probability = Length of the interval between 10.5 and 12 pounds / Total length of the interval from 6 to 12 pounds
= 1.5 pounds / 6 pounds
= 0.25

Therefore, the probability that a person on this diet loses between 10.5 and 12 pounds in the first two months is 0.25 or 25%.