To construct a binomial probability distribution, we need to follow these steps:
1. Identify the number of trials [tex]\( n = 6 \)[/tex].
2. Identify the probability of success for a single trial [tex]\( p = 0.5 \)[/tex].
The binomial probability formula is given by:
[tex]\[ P(X = x) = \binom{n}{x} p^x (1-p)^{n-x} \][/tex]
Based on this information, we can create the distribution table by calculating the probabilities [tex]\( P(x) \)[/tex] for [tex]\( x = 0, 1, 2, 3, 4, 5, 6 \)[/tex].
Given the parameters [tex]\( n = 6 \)[/tex] and [tex]\( p = 0.5 \)[/tex], the probabilities were determined for each possible value of [tex]\( x \)[/tex].
Here is the completed probability distribution table rounded to four decimal places:
\begin{tabular}{cc|c}
[tex]$x$[/tex] & [tex]$P(x)$[/tex] & \\
\hline
0 & 0.0156 & \\
\hline
1 & 0.0938 & \\
\hline
2 & 0.2344 & \\
\hline
3 & 0.3125 & \\
\hline
4 & 0.2344 & \\
\hline
5 & 0.0938 & \\
\hline
6 & 0.0156 & \\
\hline
\end{tabular}
This table represents the binomial probability distribution for [tex]\( n = 6 \)[/tex] trials and a probability of success [tex]\( p = 0.5 \)[/tex] per trial, with each probability rounded to four decimal places as requested.
