In a binomial experiment with $n=20$ trials and probability of success $p=0.70$, what is the expected value (mean) of the number of successes?

• A. $7$
• B. $6$
• C. $14$
• D. $13$

Answer: (C)

Verified step by step guidance

1. Identify the parameters of the binomial distribution: the number of trials \(n = 20\) and the probability of success in each trial \(p = 0.70\).
2. Recall the formula for the expected value (mean) of a binomial distribution, which is given by \(\text{E}(X) = n \times p\).
3. Substitute the known values into the formula: \(\text{E}(X) = 20 \times 0.70\).
4. Perform the multiplication to find the expected number of successes (do not calculate the final value here, just set up the expression).
5. Interpret the result as the average number of successes you would expect over many repetitions of the experiment.