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GRE Quantitative Reasoning QUESTION #8160
Question 1

A random variable $Y$ follows a normal distribution with mean $200$ and standard deviation $10$. Compare:

Quantity A: The probability that $Y > 220$

Quantity B: $\dfrac{1}{6}$

  • Quantity A is greater
  • Quantity B is greater✔️
  • The two quantities are equal
  • The relationship cannot be determined from the information given
Correct Answer Explanation

The value $220$ is $\dfrac{220 - 200}{10} = 2$ standard deviations above the mean.

For a standard normal distribution, the probability that $Z > 2$ is approximately $0.0228$ (about $2.28\%$).

Quantity B $= \dfrac{1}{6} \approx 0.1667$.

Since $0.0228 < 0.1667$, Quantity A is less than Quantity B.

Therefore Quantity B is greater.