Option C: np is the expression used for calculating the mean of a binomial distribution.
Explanation:
From the options, we need to determine the expression that is used for calculating the mean of a binomial distribution.
<u>Option A: npq</u>
The variance of the binomial distribution can be calculated using the expression npq.
Hence, Option A is not the correct answer.
<u>Option B: </u>
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The standard deviation of the binomial distribution can be calculated using the expression 
Hence, Option B is not the correct answer.
<u>Option C: np</u>
The mean of the binomial distribution can be calculated using the expression np
Hence, Option C is the correct answer.
<u>Option D</u>: ![\sum\left[x^{2} \cdot P(x)\right]-\mu^{2}](https://tex.z-dn.net/?f=%5Csum%5Cleft%5Bx%5E%7B2%7D%20%5Ccdot%20P%28x%29%5Cright%5D-%5Cmu%5E%7B2%7D)
The mean of the binomial distribution cannot be determined using the expression ![\sum\left[x^{2} \cdot P(x)\right]-\mu^{2}](https://tex.z-dn.net/?f=%5Csum%5Cleft%5Bx%5E%7B2%7D%20%5Ccdot%20P%28x%29%5Cright%5D-%5Cmu%5E%7B2%7D)
Hence, Option D is not the correct answer.