Question

a real number between 1 and 11 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 1 and 7 is picked. (b) find the probability that a real number between 1 and 9 is picked.

Explanation:

Step1: Recall probability - area relationship

In a probability distribution, the probability of an event is equal to the area of the corresponding region under the curve.

Step2: Find probability for part (a)

For a real number between \(1\) and \(7\), the corresponding region is \(A\). So the probability \(P(1 < x<7)\) is the area of region \(A\). Given \(A = 0.60\).

Step3: Find probability for part (b)

For a real number between \(1\) and \(9\), the corresponding regions are \(A\) and \(B\). Using the formula \(P(1 < x<9)=P(1 < x<7)+P(7 < x<9)\). Since \(P(1 < x<7)\) is the area of \(A\) (\(0.60\)) and \(P(7 < x<9)\) is the area of \(B\) (\(0.30\)), then \(P(1 < x<9)=0.60 + 0.30\).

Answer:

(a) \(0.60\)
(b) \(0.90\)