Option C: np is the expression used for calculating the mean of a binomial distribution.
Step-by-step explanation:
From the options, we need to determine the expression that is used for calculating the mean of a binomial distribution.
Option A: npq
The variance of the binomial distribution can be calculated using the expression npq.
Hence, Option A is not the correct answer.
Option B:

The standard deviation of the binomial distribution can be calculated using the expression

Hence, Option B is not the correct answer.
Option C: np
The mean of the binomial distribution can be calculated using the expression np
Hence, Option C is the correct answer.
Option D:
![\sum\left[x^(2) \cdot P(x)\right]-\mu^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/8ewfor29ca6lbq1rqo8l4mmf4jj0amyuhd.png)
The mean of the binomial distribution cannot be determined using the expression
![\sum\left[x^(2) \cdot P(x)\right]-\mu^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/8ewfor29ca6lbq1rqo8l4mmf4jj0amyuhd.png)
Hence, Option D is not the correct answer.