For each probability and percentile problem, draw the picture. 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 6 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. † Part (h) Suppose it is known that the individual lost more than 10 pounds in a month. Find the probability that he lost less than 13 pounds in the month. (Enter an exact number as an integer, fraction, or decimal.) Part (i) State "P(7 < X < 13 | X > 11) = ___" in a probability question. What is the probability that the weight loss is exactly 7 or 13 pounds given that it is greater than 11 pounds? What is the probability that the weight loss is greater than 11 pounds given that it is between 7 and 13 pounds? What is the probability that the weight loss is between 7 and 13 pounds given that it is greater than 11 pounds? What is the probability that the weight loss is below 7 pounds or above 13 pounds given that it is greater than 11 pounds? What is the probability that the weight loss is greater than 11 pounds given that it is below 7 pounds or above 13 pounds? Draw the picture and find the probability. (Enter your answer as a fraction.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
For each
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 6 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. †
Part (h)
Part (i)
- What is the probability that the weight loss is exactly 7 or 13 pounds given that it is greater than 11 pounds?
- What is the probability that the weight loss is greater than 11 pounds given that it is between 7 and 13 pounds?
- What is the probability that the weight loss is between 7 and 13 pounds given that it is greater than 11 pounds?
- What is the probability that the weight loss is below 7 pounds or above 13 pounds given that it is greater than 11 pounds?
- What is the probability that the weight loss is greater than 11 pounds given that it is below 7 pounds or above 13 pounds?
Draw the picture and find the probability. (Enter your answer as a fraction.)
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