Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches and standard deviation of 0.03 inches. The inner diameter of bearings in another lot have a mean of 0.255 inches and standard deviation of 0.002 inches. a) Find the mean and standard deviation of clearances between shafts and bearings selected from these lots. b) If a shaft and bearings are selected at random, find the probability that the shaft will not fit inside the bearings. Assume that both dimensions are normally distributed. Q3: Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches andstandard deviation of 0.03 inches. The inner diameter of bearings in another lot have amean of 0.255 inches and standard deviation of 0.002 inches.a) Find the mean and standard deviation of clearances between shafts and bearingsselected from these lots.b) If a shaft and bearings are selected at random, find the probability that the shaft willnot fit inside the bearings. Assume that both dimensions are normally distributed.

Let, X = The diameter of meter shafts Y = The inner diameter of bearings D = Y - X Given that,…

Answered: Suppose that the diameter of meter…

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches and standard deviation of 0.03 inches. The inner diameter of bearings in another lot have a mean of 0.255 inches and standard deviation of 0.002 inches. a) Find the mean and standard deviation of clearances between shafts and bearings selected from these lots. b) If a shaft and bearings are selected at random, find the probability that the shaft will not fit inside the bearings. Assume that both dimensions are normally distributed.

Q3: Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches and
standard deviation of 0.03 inches. The inner diameter of bearings in another lot have a
mean of 0.255 inches and standard deviation of 0.002 inches.
a) Find the mean and standard deviation of clearances between shafts and bearings
selected from these lots.
b) If a shaft and bearings are selected at random, find the probability that the shaft will
not fit inside the bearings. Assume that both dimensions are normally distributed.

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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