Problem

A real number between 2 and 7 will be picked according to the probability distribution shown in the figure. Regions under the curve are labeled with $A, B$, and $C$. The area of each region is shown in the table.

Use the figure and the table to answer the parts below.
(a) Find the probability that a real number between 4 and 6 is picked.
(b) Find the probability that a real number between 4 and 7 is picked.
\begin{tabular}{|cc|}
\hline Region & Area \\
\hline$A$ & 0.32 \\
$B$ & 0.56 \\
$C$ & 0.12 \\
\hline
\end{tabular}

Answer

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Answer

Final Answer: \(\boxed{0.68}\) is the probability that a real number between 4 and 7 is picked.

Steps

Step 1 :Given the areas of regions A, B, and C as 0.32, 0.56, and 0.12 respectively, the total area under the curve is 1.0.

Step 2 :For part (a), the range of real numbers between 4 and 6 falls within region B. Therefore, the probability is the area of region B divided by the total area, which is 0.56.

Step 3 :For part (b), the range of real numbers between 4 and 7 falls within regions B and C. Therefore, the probability is the sum of the areas of regions B and C divided by the total area, which is 0.68.

Step 4 :Final Answer: \(\boxed{0.56}\) is the probability that a real number between 4 and 6 is picked.

Step 5 :Final Answer: \(\boxed{0.68}\) is the probability that a real number between 4 and 7 is picked.

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