Final answer:
In a Poisson distribution, the standard deviation is the square root of the mean. Given a mean of 9, the standard deviation is √9 = 3, which corresponds to option (a).
Step-by-step explanation:
The question involves a Poisson distribution which is a probability distribution that measures the probability of a given number of events happening in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event.
In a Poisson distribution, the mean (μ) is equal to the variance (σ²). Therefore, the standard deviation (σ) is the square root of the mean.
Given that the mean (μ) is 9 for the biased coin tossing, we calculate the standard deviation by taking the square root of the mean:
σ = √μ = √9 = 3
The standard deviation for this distribution is 3, which corresponds to option (a).