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.
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: [tex]\sqrt{npq}[/tex]
The standard deviation of the binomial distribution can be calculated using the expression [tex]\sqrt{npq}[/tex]
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: [tex]\sum\left[x^{2} \cdot P(x)\right]-\mu^{2}[/tex]
The mean of the binomial distribution cannot be determined using the expression [tex]\sum\left[x^{2} \cdot P(x)\right]-\mu^{2}[/tex]
Hence, Option D is not the correct answer.