A CNC (computer numerical control) machine produces iron automobile crankshafts. Samples are measured and the inner diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. For all computations, assume an approximately normal distribution. The sample mean and standard deviation for the given data are = 1.0056, and s = 0.0246. Find a 99% confidence interval on the mean of diameter. Compute a 99% prediction interval on a measured diameter of a single crankshaft piece taken from the machine. Find the 99% tolerance limits that will contain most of the metal pieces produced by the CNC machine. a. CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175) b. Insufficient data to compute. Missing the sample size n c. CI on the mean: 0.970 < μ < 1.9845. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175) d. CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175). Insufficient data to compute for the Tolerance Interval
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A CNC (computer numerical control) machine produces iron automobile crankshafts. Samples are measured and the inner diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. For all computations, assume an approximately
Find a 99% confidence interval on the mean of diameter. Compute a 99% prediction interval on a measured diameter of a single crankshaft piece taken from the machine. Find the 99% tolerance limits that will contain most of the metal pieces produced by the CNC machine.
| a. |
CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175) |
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| b. |
Insufficient data to compute. Missing the |
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| c. |
CI on the mean: 0.970 < μ < 1.9845. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175) |
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| d. |
CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175). Insufficient data to compute for the Tolerance Interval |
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