A machining operation at Cleveland Tool Works (Process A) produces small parts, 10% of which are defective. A similar operation (Process B) produces small but unrelated parts. Process B is considered to be in control if it produces no more than 10% defective units. Sampling for Process A consists of selecting 20 units at specific intervals. Sampling for Process B is similar with a sample size of 15 units.
a. Determine the probability of finding not more than 1 defective unit in a sample from Process A.
b. Determine the probability that Process B will be stopped needlessly when it is producing 5% defective units.
An economist, working in the Center for Economic Studies at the University of Michigan, believes that during periods of high economic growth in the United States, the U.S. dollar appreciates with probability 0.70; in periods of moderate economic growth, the dollar with probability 0.40; and during periods of low economic growth, the dollar appreciates with probability 0.20. During any period of time, the probability of high economic growth is 0.30, the probability of moderate growth is 0.50, and the probability of low economic growth is 0.20.
a. Assuming the U.S. dollar has been appreciating during the present period, and assuming that the economist is correct, determine the probabilities that the U.S. is experiencing a period of high, moderate, and low economic growth.
b. Assuming the U.S. dollar has been depreciating during the present period, and assuming that the economist is correct, determine the probabilities that the U.S. is experiencing a period of high, moderate, and low economic growth.
The probability of defective unions for Cleveland Tool Works is determined.