A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%. What is the standard deviation of X, the number of patients seen until an injection-site reaction occurs?

X follows a geometric distribution, since it counts the number of patients seen until the first reaction. For this distribution, the standard deviation is √(1 − p) / p. With p = 0.11, this is √0.89 / 0.11 ≈ 8.5763, so the correct choice is 8.5763.

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