Chapter 11.4, Problem 32PPS

To determine

To find the most likely number of successes.

Answer to Problem 32PPS

  $\boxed{7}$

Explanation of Solution

Given information:

Each binomial distribution has $n$ trials and $p$ probability of success. Determine the most likely number of successes.

  $n=12,$

  $p=0.55$

Calculation:

Here, we will consider the following attributes for a binomial distribution:

  $n=12,$

  $p=0.55$

Generally, the mean $\mu$ or the most likely number of successes, of any binomial distribution is:

  $\mu =np$

Thus, is the $n$ number of trials and $p$ is the probability of success.

Now, substitute in $n=12,$

  $p=0.55$ the above expression to find the most likely number of successes,

  $\mu =np$

  $\begin{array}{l}\mu =12\times 0.55\\ \mu =6.6\\ \mu \approx 7\end{array}$

Hence, the most likely number of successes is $\boxed{7}$ .