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To find the expected value \( E(X) \), you multiply each outcome 'x' by its corresponding probability \( P(X=x) \) and then sum up all these products. Using the data provided:

\( E(X) = \sum [x \cdot P(X=x)] \)

\( E(X) = (4 \times 0.2) + (5 \times 0.2) + (6 \times 0.1) + (7 \times 0.1) + (8 \times 0.4) \)

Now, calculating each term:

\( E(X) = (0.8) + (1.0) + (0.6) + (0.7) + (3.2) \)

\( E(X) = 6.3 \)

Therefore, the expected value \( E(X) \) is 6.3. Since the instruction is to round to one decimal place, the final answer remains 6.3.

Consider the following data:
x
4
0.2
5
0.2
6
0.1
7
0.1
8
0.4
step 1 of 5:
Find the expected value E(X). Round your answer to one decimal place.
