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Anyone know how to solve this on a calc for NcR?
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:
(A) 35 % ✘
(B) 65 %
(C) 75 %
Explanation:
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
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Hi @pcunniff – there’s the nCr function in BA II Plus calculators on top of the “+” sign.
So for “8 choose 7”, i.e. 8C7, here are the keystrokes which should get you the answer 8: 8 [2ND] [+] 7 =
For “8 choose 8”, i.e. 8C8, the answer is 1 (without the need to do the calculations), because there is only 1 way to choose 8 items out of 8. But just in case the keystrokes here follow the same principle (which should give you 1): 8 [2ND] [+] 8 =
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