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MMLU-Pro / 8199 / Suppose there are 10 independent random variables X₁,X₂,⋯,X₁0. Each…

Problem

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

question

Suppose there are 10 independent random variables X1,X2,⋯,X10X_1, X_2, \cdots, X_10. Each of the XiX_i lies within the range of [10, 11] with a mean value of 10.5. If we take the mean of the 10 random variables as Xn^\hat{X_n}. What is the upper bound of the probability that Xn^\hat{X_n} is either smaller than 10.2 or larger than 10.8?
Plain-text mathematical notation (without MathML)
Suppose there are 10 independent random variables X₁,X₂,⋯,X₁0. Each of the X_(i) lies within the range of [10, 11] with a mean value of 10.5. If we take the mean of the 10 random variables as (X_(n))^. What is the upper bound of the probability that (X_(n))^ is either smaller than 10.2 or larger than 10.8?
Original LaTeX notation
Suppose there are 10 independent random variables $X_1, X_2, \cdots, X_10$. Each of the $X_i$ lies within the range of [10, 11] with a mean value of 10.5. If we take the mean of the 10 random variables as $\hat{X_n}$. What is the upper bound of the probability that $\hat{X_n}$ is either smaller than 10.2 or larger than 10.8?

category

math

options

  1. 0.1000
  2. 0.3912
  3. 0.5999
  4. 0.2456
  5. 0.2857
  6. 0.6731
  7. 0.4256
  8. 0.1573
  9. 0.5123
  10. 0.3305

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8199
task_id
1036a90d-b5d7-511a-99ae-83ef18971113
task_key
default--test--8199
task_revision_id
1
config / split
default / test

Official source

initial import