I have a total of three different answers that I got and had help with and nothing definitive. One way that I figured it out I received 4/7. I asked two other people and they gave me two completely different answers.
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
To find the probability that a person on this diet loses less than 10 pounds in the first two months, you need to determine the proportion of the interval 6 to 12 pounds that is less than 10 pounds.
Since the weight loss has a uniform distribution, you can visualize it as a rectangle with a base of 12 - 6 = 6 pounds and a height of 1/6 since this represents the probability density function (PDF) for a uniform distribution.
To find the probability, you need to calculate the area of the region that corresponds to losing less than 10 pounds.
First, determine the length of this region. Since the uniform distribution is continuous, you can calculate it as the difference between the target weight loss (10 pounds) and the starting weight loss (6 pounds), which is 10 - 6 = 4 pounds.
Next, calculate the area of this region by multiplying the length by the height of the rectangle: 4 * 1/6 = 2/3.
Therefore, the probability of a person on this diet losing less than 10 pounds in the first two months is 2/3.
So the correct answer is D) 2/3.