Question

using the graph of a distribution to find probabilities: basic
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: Recall the property of probability distribution

The probability of an event is equal to the sum of the areas of the regions corresponding to that event.

Step2: Solve part (a)

For the probability that a real - number between \(0\) and \(6\) is picked, we need to sum the areas of regions \(A\) and \(B\).
\(P(0\lt X\lt6)=A + B\)
Substitute \(A = 0.15\) and \(B=0.45\) into the formula:
\(P(0\lt X\lt6)=0.15 + 0.45=0.6\)

Step3: Solve part (b)

For the probability that a real - number between \(3\) and \(8\) is picked, we need to sum the areas of regions \(B\) and \(C\).
\(P(3\lt X\lt8)=B + C\)
Substitute \(B = 0.45\) and \(C = 0.30\) into the formula:
\(P(3\lt X\lt8)=0.45+0.30 = 0.75\)

Answer:

(a) \(0.6\)
(b) \(0.75\)