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According to a study by Dr. John McDougall of his live-in weight loss program at St....

According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let's suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month.
a. Find the probability that the individual lost more than 12 pounds in a month. (Enter an exact number as an integer, fraction, or decimal.)

b. Suppose it is known that the individual lost more than 8 pounds in a month. Find the probability that he lost less than 12 pounds in the month. (Enter an exact number as an integer, fraction, or decimal.)

Math   Statistics-And-Probability   
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Answer #1

Let X is a random variable shows the individual lost pounds in a month. Here X has Uniform distribution between 6 and 15 so pdf of X is

(a)

The probability that the individual lost more than 12 pounds in a month is

(b)

And

So the probability that he lost less than 12 pounds in the month given that  the individual lost more than 8 pounds in a month is

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