Answered: Probability distribution.The…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Probability distribution.
The pharmaceutical manufacturing process is continually monitored for out-of-specs
content of the active ingredient in aspirin. Every hour 5 samples are taken from the
process. Listed below are the number of out-of-specs aspirin pills in a sample of 5, and
the probability associated with each.
Out-of-specs (x) Probability P(x) x · P(x) x - μ (x - μ)² (x-μ)²P(x)
0 0.9525
1 0.0380
2 0.0078
3 0.0015
4 0.0002
5 0
Answer the following questions by completing the columns of the above table.
a) Calculate the expected number of out-of-specs aspirin pills per hour (mean).

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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