Chapter 11.4, Problem 34PPS

To determine

To find the most likely numbers of successes.

Answer to Problem 34PPS

  $\boxed{4}$

Explanation of Solution

Given information:

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

  $n=11,p=0.35$

Calculation:

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

  $n=11,p=0.35$

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

  $\mu =np$

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

Now, substitute $n=11,p=0.35$ in the above expression to find the most likely number of successes,

  $\mu =np$

  $\begin{array}{l}\mu =11\times 0.35\\ \mu =3.85\\ \mu \approx 4\end{array}$

Hence, the most likely number of successes is $\boxed{4}$ .