Manufacture of a certain component requires threedifferent machining operations. Machining time foreach operation has a normal distribution, and the threetimes are independent of one another. The mean valuesare 15, 30, and 20 min, respectively, and the standarddeviations are 1, 2, and 1.5 min, respectively. What isthe probability that it takes at most 1 hour of machiningtime to produce a randomly selected component?
Manufacture of a certain component requires threedifferent machining operations. Machining time foreach operation has a normal distribution, and the threetimes are independent of one another. The mean valuesare 15, 30, and 20 min, respectively, and the standarddeviations are 1, 2, and 1.5 min, respectively. What isthe probability that it takes at most 1 hour of machiningtime to produce a randomly selected component?
Manufacture of a certain component requires threedifferent machining operations. Machining time foreach operation has a normal distribution, and the threetimes are independent of one another. The mean valuesare 15, 30, and 20 min, respectively, and the standarddeviations are 1, 2, and 1.5 min, respectively. What isthe probability that it takes at most 1 hour of machiningtime to produce a randomly selected component?
Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal distribution, and the three times are independent of one another. The mean values are 15, 30, and 20 min, respectively, and the standard deviations are 1, 2, and 1.5 min, respectively. What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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