Question 1 through 4: Assume that an automatic lathe may produce parts with some flaws. The number of flaws per part is a random variable satisfying the following probability distribution: X 0 1 2 3 4 P 0.2 0.16 0.22 0.2 1. Find the average number of flaws per part produced by this lathe. (A) 2.09 (B) 2.34 (C) 2.08 (D) 2.03 E 1.61 2. A part will be labeled unqualified if it has more than two flaws. If a random sample of 13 parts is selected, find the probability that there are not more than 2 unqualified parts. A 0.0431 B 0.0481 0.0711 (D) 0.0311 E 0.1461 3. A random sample of 600 parts is selected. Let X; be the number of flaws on i-th part. Assume that these random variables are independent, find the standard deviation of the sample mean. 0.1554 0.0095 0.1545 D 0.1128 E 0.0582 4. Find the probability that the average number of flaws for this sample of 600 parts is between 2 and 2.2. A 0.8279 0.8957 0.447 D 0.8931 E 0.7146