A portfolio manager has a tight tracking error of 50 basis points. The manager expects to be within this tracking error for a given quarter 85% of the time. If that expectation is correct and each quarter is independent, the probability that the manager is within the tracking error for at least 7 of the next 8 quarters is closest to:35%65%75%

We will use a binomial distribution with p = 0.85 and n = 10. We want to calculate: Pr(X >= 7) = Pr(X = 7) + Pr(X = 8) Pr(X = 7) = (8 choose 7) * (0.85)^7 * (1 – 0.85)^(8 - 7) = 0.3847 Pr(X = 8) = (8 choose 8) * (0.85)^8 * (1 – 0.85)^(8 - 8) = 0.2725 Pr(X >= 7) = 0.3847 + 0.2725 = 0.6572

> @AdaptPrep said: > We will use a binomial distribution with p = 0.85 and n = 10. We want to calculate: You said you set n = 10, did you not mean n = 8?

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- AdaptPrep
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  06 Oct 2018 at 7:30 pm
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  We will use a binomial distribution with p = 0.85 and n = 10. We want to calculate:
  
  Pr(X >= 7)
  = Pr(X = 7) + Pr(X = 8)
  
  Pr(X = 7) = (8
  choose 7) * (0.85)^7 * (1 – 0.85)^(8 – 7) = 0.3847
  
  Pr(X = 8) = (8
  choose 8) * (0.85)^8 * (1 – 0.85)^(8 – 8) = 0.2725
  
  Pr(X >= 7)
  = 0.3847 + 0.2725 = 0.6572
- aaronpcjb
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  - CFA Level 1
  13 Oct 2018 at 5:31 pm
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  > @AdaptPrep said:
  > We will use a binomial distribution with p = 0.85 and n = 10. We want to calculate:
  
  You said you set n = 10, did you not mean n = 8?
- AdaptPrep
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  - Undecided
  13 Oct 2018 at 7:56 pm
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  Yes, we meant n = 8, not 10. Good catch!
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