Problem 82A
A wildlife biologist wished to estimate the median weight of bears in Alaska. The weights of the bear population he studied follow a continuous distribution with an unknown median . He captured a sample of 15 bears. Let be the weight (in pounds) of the fifth smallest bear in the sample of 15 captured bears. Let be the weight (in pounds) of the fifth largest bear in the sample.
Calculate the probability that the median is between and , i.e., .
Problem 82B
The wildlife biologist in Problem 82A also wishes to estimate , the seventy fifth percentile of the weights of bear population he studied. Let be the weight of the tenth smallest bear in the sample of 15 captured bears. Let be the weight of the second largest bear in the sample of 15 bears.
Calculate the probability that is between and , i.e., .
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