Assume that the weight loss for the first two months of a diet program has a uniform distrbiution

over the interval 6 to 12 pounds. Find the probability that a person on this diet loses less than 10
pounds in the first two months.

Not sure what to do.

A) 1/6
B) 5/7
C) 1/3
D) 2/3

The answer is 2/3.

[10-6]/[12-6] = 4/6 =2/3

From your data, there is possibility of losing 6, 7, 8, 9, 10, 11, or 12 pounds. "Less than 10 pounds" includes 6, 7, 8 and 9 pounds lost.

I get 4/7. However,if you say ≤ 10, then it would be 5/7.

I do not know what to do. I used the Venn diagram for myself but I think I was wrong as I got 4/7 as PsyDag did. I don't think 5/7 is correct as the problem doesn't say equal to or less than 10. I do not understand Adam's equation and solution. Could you please help me understand?

To find the probability that a person on this diet loses less than 10 pounds in the first two months, we will use the uniform distribution over the interval from 6 to 12 pounds.

First, let's find the probability density function (PDF) of the uniform distribution. Since the distribution is uniform, the PDF is simply a constant value across the range of the distribution.

The range of the distribution is from 6 to 12 pounds, so the length of this interval is 12 - 6 = 6 pounds.

The PDF is given by the formula: f(x) = 1 / (b - a), where a is the lower bound of the interval (6 pounds) and b is the upper bound of the interval (12 pounds). Plugging in the values, we have f(x) = 1 / 6.

Now, let's find the probability that a person loses less than 10 pounds in the first two months.

Since the distribution is uniform, the probability of an event occurring within a certain range is equal to the length of that range divided by the total length of the distribution.

To calculate the probability of losing less than 10 pounds, we need to find the length of the interval from 6 pounds to 10 pounds.

The length of this interval is 10 - 6 = 4 pounds.

Now, we divide this length by the total length of the distribution (6 pounds) to get the probability.

So, the probability of losing less than 10 pounds in the first two months is 4 / 6 = 2 / 3.

Therefore, the correct answer is option D) 2/3.