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