Final Answer:
The probability distribution of x, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width than the average number of imperfections per 10 meters of this fabric 1.137. The final answer is b) 1.137.
Step-by-step explanation:
The average number of imperfections per 10 meters of synthetic fabric is calculated using the expected value of the probability distribution. In this case, it involves multiplying each possible number of imperfections by its probability and summing up these values. The formula for expected value (E) is given by E(x) = Σ [x * P(x)], where x represents the number of imperfections, and P(x) is the probability of x imperfections. After performing the calculations based on the provided probability distribution, the result is an average of 1.137 imperfections per 10 meters.
To elaborate, each possible outcome (number of imperfections) is multiplied by its probability and added together. This mathematical process reflects the concept of expected value, representing the average outcome over many trials. In the context of synthetic fabric production, it provides insight into the typical number of imperfections one can expect in a continuous roll of uniform width.
The final answer is b) 1.137.