Question

a real number between 0 and 6 will be picked according to the probability distribution shown in the figure. regions under the curve are labeled with a, b, c, and d. 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 2 and 5 is picked. (b) find the probability that a real number between 4 and 6 is picked.

Explanation:

Step1: Identify relevant regions for (a)

For a number between 2 and 5, the relevant regions are $B$ and $C$.

Step2: Calculate probability for (a)

$P(2 < x<5)=P(B)+P(C)=0.48 + 0.20=0.68$

Step3: Identify relevant regions for (b)

For a number between 4 and 6, the relevant regions are $C$ and $D$.

Step4: Calculate probability for (b)

$P(4 < x<6)=P(C)+P(D)=0.20+ 0.08 = 0.28$

Answer:

(a) $0.68$
(b) $0.28$