In a study on the effectiveness of different flu vaccines, four vaccines were tested with the following probabilities of preventing the flu:

Is this a probability distribution, and if so, what are its mean and standard deviation?

• A. No, this is not a valid probability distribution because the sum of the probabilities is $0.9$.
• B. No, this is not a valid probability distribution because one of the probabilities is greater than $1$.
• C. Yes, this is a valid probability distribution with $\mu =0.34$ and $\sigma =0.1624$.
• D. Yes, this is a valid probability distribution with $\mu =0.1624$ and $\sigma =0.34$.

Answer: (A)