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MMLU-Pro / 7784 / 5.5-9. Suppose that the length of life in hours (say, X ) of a light bulb…

Problem

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

question

5.5-9. Suppose that the length of life in hours (say, XX ) of a light bulb manufactured by company AA is N(800,14400)N(800,14400) and the length of life in hours (say, YY ) of a light bulb manufactured by company BB is N(850,2500)N(850,2500). One bulb is randomly selected from each company and is burned until "death." (a) Find the probability that the length of life of the bulb from company AA exceeds the length of life of the bulb from company BB by at least 15 hours.
Plain-text mathematical notation (without MathML)
5.5-9. Suppose that the length of life in hours (say, X ) of a light bulb manufactured by company A is N(800,14400) and the length of life in hours (say, Y ) of a light bulb manufactured by company B is N(850,2500). One bulb is randomly selected from each company and is burned until "death."
(a) Find the probability that the length of life of the bulb from company A exceeds the length of life of the bulb from company B by at least 15 hours.
Original LaTeX notation
5.5-9. Suppose that the length of life in hours (say, $X$ ) of a light bulb manufactured by company $A$ is $N(800,14400)$ and the length of life in hours (say, $Y$ ) of a light bulb manufactured by company $B$ is $N(850,2500)$. One bulb is randomly selected from each company and is burned until "death."
(a) Find the probability that the length of life of the bulb from company $A$ exceeds the length of life of the bulb from company $B$ by at least 15 hours.

category

math

options

  1. $0.3498$
  2. $0.1256$
  3. $0.2187$
  4. $0.3085$
  5. $0.3654$
  6. $0.4112$
  7. $0.5000$
  8. $0.4256$
  9. $0.2753$
  10. $0.1587$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
7784
task_id
6261fda7-fb23-59d4-b50a-7975e5b3fa22
task_key
default--test--7784
task_revision_id
1
config / split
default / test

Official source

initial import