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A hedge fund returns on average 26% per year with a standard deviation of 12%. Using the empirical rule, approximate the probability the fund returns over 50% next year

Respuesta :

Answer:

0.025 is the probability that the fund returns over 50% next year.

Explanation:

We are given the following information in the question:

Mean, μ = 26%

Standard Deviation, σ = 12%

Empirical Formula:

  • Almost all the data lies within three standard deviation from the mean for a normal data.
  • About 68% of data lies within one standard deviation of the mean.
  • Around 95% of data lies within two standard deviation of the mean.
  • About 99.7% of data lies within three standard deviations of mean.
  • The mean divide the data into two equal parts.

We have to find the approximate probability of the fund returns over 50% next year.

[tex]P(x > 50)\\=P(x > 26\% + 2(12\%))\\=P(x > \mu + 2\sigma)\\\\=0.5 - \dfrac{P(\mu + 2\sigma <x < \mu + 2\sigma)}{2}\\\\=0.5 - \dfrac{0.95}{2}\\\\=0.025[/tex]

0.025 is the probability that the fund returns over 50% next year.

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