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qid 8010 · math

Question: A soft drink dispenser can be adjusted to deliver any fixed number of ounces. If the machine is operating with a standard deviation in delivery equal to 0.3 ounce, what should be the mean setting so that a 12-ounce cup will overflow less than 1% of the time? Assume a normal distribution for ounces delivered.

  1. 12 + 0.99(0.3) ounces
  2. 12 - 1.645(0.3) ounces
  3. 12 + 2.326(0.3) ounces
  4. 12 - 1.96(0.3) ounces
  5. 12 + 2.576(0.3) ounces
  6. 12 + 1.645(0.3) ounces
  7. 12 - 0.99(0.3) ounces
  8. 12 - 2.576(0.3) ounces
  9. 12 + 1.96(0.3) ounces
  10. 12 - 2.326(0.3) ounces

Our answer: J. 12 - 2.326(0.3) ounces Source quote machine-checked (exact quote)

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How it was answered

Multi-step solver (maze), replayed by code

card: maze · card sha256 e1de1dcb1be6e0fe…

Current source

NIST/SEMATECH e-Handbook of Statistical Methods, "Critical Values of the Standard Normal Distribution"

https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm

“The table below contains the area under the standard normal curve from 0 to z. This can be used to compute the cumulative distribution function values for the standard normal distribution.”

Source quote machine-checked (exact quote)

retrieved 2026-09-18T01:08:17.367Z

page text sha256 bbfa953636ad569f… · content sha256 86d49ee9c96b34ef…

addendum maze_qid8010_b4_maze_input_ADDENDUM_source_rs20260918T010817Z · sha256 60c8c75d5d50f6b0… · replaces the version below, addendum sha256 6a899e1c6cb82b07…

Earlier version (superseded)

https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm

Source weak (http_get_200_text_and_question_terms)

retrieved 2026-09-17T23:24:30.954Z

page text sha256 3f1d2d36940d41a0… · content sha256 —

addendum maze_qid8010_b4_maze_input_ADDENDUM_source_bf20260917T232430Z · sha256 6a899e1c6cb82b07… · replaces the version below, addendum sha256 0696eab50f7bcb8f…

Earlier version (superseded)

No public source has been found for this card yet (3 places checked internally).

addendum maze_qid8010_b4_maze_input_ADDENDUM_source · sha256 0696eab50f7bcb8f…

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