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 more than 11 pounds in the first two months.
Prob(11 or 12)=2/6
To find the probability that a person on this diet loses more than 11 pounds in the first two months, we need to determine the probability of the weight loss falling within the range of 6 to 12 pounds.
In this case, we have a uniform distribution, which means that the probability density function (pdf) is constant within the defined interval of 6 to 12 pounds. To find the probability, we first need to calculate the total interval length.
Interval length = upper bound - lower bound = 12 - 6 = 6 pounds
Since the distribution is uniform, the density within this interval is constant, which means that the probability density is given by:
density = 1 / interval length = 1 / 6
To find the probability of losing more than 11 pounds, we need to calculate the area of the probability distribution curve in the range above 11 pounds. Since the distribution is uniform, this is equivalent to finding the proportion of the interval length above 11 pounds.
Length above 11 pounds = (upper bound - 11) = 12 - 11 = 1 pound
Therefore, the probability of losing more than 11 pounds is:
probability = length above 11 pounds / interval length = 1 / 6
Therefore, the probability that a person on this diet loses more than 11 pounds in the first two months is 1/6 or approximately 0.1667.