Suppose X follows a binomial distribution with n=30 trials and p=0.5 probability of success . Find μₓ, the mean of X. Do not round your answer.2 points

1. Break Down the Problem

To find the mean of a binomial distribution, we will use the formula for the mean $\mu_X$. Given that $n$ (number of trials) is 30 and $p$ (probability of success) is 0.5, we will apply this information into the formula.

2. Relevant Concepts

The mean of a binomial distribution is calculated using the formula: $\mu_X = n \cdot p$

3. Analysis and Detail

Now, substituting the given values into the formula:

• $n = 30$
• $p = 0.5$

Calculating the mean: $\mu_X = 30 \cdot 0.5$

4. Verify and Summarize

Calculating: $\mu_X = 15$

The mean of the binomial distribution in this case is 15, which indicates that, on average, there are 15 successes in 30 trials with a success probability of 0.5.

Final Answer

$\mu_X = 15$