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MMLU-Pro / 8770 / 5.5-7. Suppose that the distribution of the weight of a prepackaged "1-pound…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

5.5-7. Suppose that the distribution of the weight of a prepackaged "1-pound bag" of carrots is N(1.18,0.072)N\left(1.18,0.07^2\right) and the distribution of the weight of a prepackaged "3-pound bag" of carrots is N(3.22,0.092)N\left(3.22,0.09^2\right). Selecting bags at random, find the probability that the sum of three 1-pound bags exceeds the weight of one 3-pound bag. HInT: First determine the distribution of YY, the sum of the three, and then compute P(Y>W)P(Y>W), where WW is the weight of the 3-pound bag.
Plain-text mathematical notation (without MathML)
5.5-7. Suppose that the distribution of the weight of a prepackaged "1-pound bag" of carrots is N(1.18,0.07²) and the distribution of the weight of a prepackaged "3-pound bag" of carrots is N(3.22,0.09²). Selecting bags at random, find the probability that the sum of three 1-pound bags exceeds the weight of one 3-pound bag. HInT: First determine the distribution of Y, the sum of the three, and then compute P(Y>W), where W is the weight of the 3-pound bag.
Original LaTeX notation
5.5-7. Suppose that the distribution of the weight of a prepackaged "1-pound bag" of carrots is $N\left(1.18,0.07^2\right)$ and the distribution of the weight of a prepackaged "3-pound bag" of carrots is $N\left(3.22,0.09^2\right)$. Selecting bags at random, find the probability that the sum of three 1-pound bags exceeds the weight of one 3-pound bag. HInT: First determine the distribution of $Y$, the sum of the three, and then compute $P(Y>W)$, where $W$ is the weight of the 3-pound bag.

category

math

options

  1. $0.9800$
  2. $0.9270$
  3. $0.8750$
  4. $0.8990$
  5. $0.9100$
  6. $0.9920$
  7. $0.9830$
  8. $0.9650$
  9. $0.9500$
  10. $0.8570$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8770
task_id
39ea6c00-6eb6-5510-bed9-37dee3f4d353
task_key
default--test--8770
task_revision_id
1
config / split
default / test

Official source

initial import