Final answer:
The probability that the wood paneling ordered by a customer has a thickness less than 2 inches is 1/8.
Step-by-step explanation:
To find the probability that the wood paneling ordered by a customer has a thickness less than 2 inches, we need to use the cumulative distribution function (CDF) described in the question. The CDF is given as follows:
F(x) = 0 for x < 1/8
F(x) = 1/8 for 1/8 ≤ x < 1/4
To calculate the probability, we need to find the area under the CDF curve for the range of thickness less than 2 inches.
Since the range of thickness is from 0 to 2 inches, we can break it into two parts:
1. For x < 1/8, the probability is 0.
2. For 1/8 ≤ x < 1/4, the probability is 1/8.
The total probability is the sum of these two probabilities: 0 + 1/8 = 1/8.
The Cumulative Distribution Function (CDF) is a concept used in probability theory and statistics.
It provides the probability that a random variable takes on a value less than or equal to a specified point.
Question: The thinkness of wood paneling (in inches) that a customer orders is a random varibale with the following cumulative distribution function: F(x) for x < 1/8, F(x) for 1/8 ≤ x < 1/4.
What is the probability that the wood paneling ordered by a customer has a thickness less than 2 inches?"