Assume that the weight loss for the first tow 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 more than 11 pounds in the fisrt two months.

How do you do this, is there a formula that is used?

To find the probability that a person on this diet loses more than 11 pounds in the first two months, we need to calculate the area of the probability distribution function (PDF) that lies to the right of 11 pounds.

In this case, the weight loss for the first two months follows a uniform distribution over the interval 6 to 12 pounds. The probability density function for a uniform distribution is a constant value over the interval and zero outside the interval.

To calculate the probability, we can follow these steps:

1. Calculate the total area under the PDF. The formula to find the area under a uniform distribution is (b - a), where 'a' is the lower bound and 'b' is the upper bound of the interval.

In this case, the lower bound is 6 pounds and the upper bound is 12 pounds. So, the total area under the PDF is (12 - 6) = 6.

2. Calculate the area under the PDF for values greater than 11 pounds. Since the distribution is uniform, the area under the PDF is the same as the length of the interval from 11 to 12. Therefore, the area is (12 - 11) = 1.

3. Divide the area under the PDF for values greater than 11 pounds by the total area under the PDF to find the probability.

So, the probability that a person on this diet loses more than 11 pounds in the first two months is 1/6 or approximately 0.167.

Note that the formula used here is specific to the uniform distribution. Different probability distributions may require different formulas to calculate probabilities.