Exam P Practice Problem 82 – Estimating the Median Weight of Bears

Problem 82-A

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 M. He captured a sample of 15 bears. Let Y_5 be the weight (in pounds) of the fifth smallest bear in the sample of 15 captured bears. Let Y_{11} be the weight (in pounds) of the fifth largest bear in the sample.

Calculate the probability that the median M is between Y_5 and Y_{11}, i.e., P(Y_5<M<Y_{11}).

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.5000

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.7899

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.8218

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.8815

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.9232

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Problem 82-B

The wildlife biologist in Problem 82-A also wishes to estimate \tau_{75}, the seventy fifth percentile of the weights of bear population he studied. Let Y_{10} be the weight of the tenth smallest bear in the sample of 15 captured bears. Let Y_{14} be the weight of the second largest bear in the sample of 15 bears.

Calculate the probability that \tau_{75} is between Y_{10} and Y_{14}, i.e., P(Y_{10}<\tau_{75}<Y_{14}).

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.6155

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.7500

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.7715

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.8383

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.9232

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Answers

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\copyright \ 2014 \ \text{ Dan Ma}

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