Question

a real number between 0 and 10 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 0 and 6 is picked. (b) find the probability that a real number between 3 and 8 is picked.

Explanation:

Step1: Identify relevant regions for (a)

The regions from 0 to 6 are A and B.

Step2: Calculate probability for (a)

The probability is the sum of areas of A and B, so $P(0\leq x\leq6)=0.15 + 0.45=0.6$.

Step3: Identify relevant regions for (b)

The regions from 3 to 8 are B and C.

Step4: Calculate probability for (b)

The probability is the sum of areas of B and C, so $P(3\leq x\leq8)=0.45+ 0.30 = 0.75$.

Answer:

(a) 0.6
(b) 0.75