## To find the probabilities for the given range of pounds lost, we need to determine the total number of possibilities and the number of possibilities within the given range. Since the weight loss is uniformly distributed, we can calculate the probabilities by dividing the number of possibilities within the range by the total number of possibilities.

For the first question:

1. The weight loss is more than 10 pounds. Since the weight loss is evenly spread over the range of 6 to 12 pounds, there are two possibilities (11 and 12) out of six total possibilities (6, 7, 8, 9, 10, 11, 12). So the probability is 2/6 = 1/3 â‰ˆ 0.333.

For the second question:

2. The weight loss is between 8 pounds and 11 pounds. Within this range, there are three possibilities (8, 9, and 10) out of six total possibilities (6, 7, 8, 9, 10, 11, 12). So the probability is 3/6 = 1/2 = 0.500.

For the third question:

3. The weight loss is between 9 pounds and 12 pounds. Within this range, there are three possibilities (9, 10, 11) out of six total possibilities (6, 7, 8, 9, 10, 11, 12). So the probability is 3/6 = 1/2 = 0.500.

Now, let's move on to the next question about finding the mean (u) for the binomial distribution with given values of n and p.

For a binomial distribution, the mean (u) can be calculated using the formula u = n * p, where n is the number of trials and p is the probability of success in each trial.

In this case, n is given as 40 and p is given as 0.2.

So, u = 40 * 0.2 = 8.0

Hence, the correct answer is 8.0 for the mean (u) for the binomial distribution with n = 40 and p = 0.2.

I hope this explanation helps you understand how to solve these problems. Let me know if you have any further questions!