Problem

The probability distribution for $\mathrm{X}$ is shown below.
\begin{tabular}{|l|l|}
\hline$X$ & $P(X=x)$ \\
\hline 5 & 0.11 \\
6 & 0.18 \\
7 & 0.33 \\
8 & 0.22 \\
9 & 0.16 \\
\hline
\end{tabular}
Determine $P(X> 5)$

Answer

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Answer

So, the probability that X is greater than 5, denoted as P(X>5), is \(\boxed{0.89}\).

Steps

Step 1 :The probability distribution for X is given as follows: \begin{tabular}{|l|l|} \hline X & P(X=x) \\ \hline 5 & 0.11 \\ 6 & 0.18 \\ 7 & 0.33 \\ 8 & 0.22 \\ 9 & 0.16 \\ \hline \end{tabular}

Step 2 :We are asked to determine the probability that X is greater than 5, denoted as P(X>5).

Step 3 :This can be calculated by summing up the probabilities of X being 6, 7, 8, and 9. This is because the event X>5 is the union of the events X=6, X=7, X=8, and X=9.

Step 4 :By adding the probabilities for X=6, X=7, X=8, and X=9, we get 0.18 + 0.33 + 0.22 + 0.16 = 0.89.

Step 5 :So, the probability that X is greater than 5, denoted as P(X>5), is \(\boxed{0.89}\).

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