Probability and statics a) Control charis are to be constructed for samples of sizen=5, and i and rare computed for each 25 preliminary sanples as follors.Er= 3902 5.7=135.8. Find the trial control limits for X and R control chart.b) A random sample of size n, =16 is selected from a normal population with a mean of85 and a standard deviation of 9. A second random sample of size n =25 is taken frommother nornal population with mem 70 and standard deviation 14. Let X, and X, be teosample means. Find the probability theat X, - X, decreased by 13.c) The mannfacturing of laser printers produces 4% defective printers. Assume the chipsare independent and that a lot contains 1000 laser printers. Approxinate the probability that less than35 printers are defective.d) Suppose the random variables X and Y have the following joint probability mass function:Xy f(x,y)11 0.0511 0.1012 0.1512 0.20210.2021 0.1522 0.1022 0.05Find Conditional probability distribution of X given that Y = 1.< o O

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Description: Probability and statics a) Control charis are to be constructed for samples of sizen=5, and i and rare computed for each 25 preliminary sanples as follors.Er= 3902 5.7=135.8. Find the trial control limits for X and R control chart.b) A random sample

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Find the trial control limits for Xand R control chart.

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Probability and statics

a) Control charis are to be constructed for samples of sizen=5, and i and r
are computed for each 25 preliminary sanples as follors.
Er= 3902 5.
7=135.8. Find the trial control limits for X and R control chart.
b) A random sample of size n, =16 is selected from a normal population with a mean of
85 and a standard deviation of 9. A second random sample of size n =25 is taken from
mother nornal population with mem 70 and standard deviation 14. Let X, and X, be teo
sample means. Find the probability theat X, - X, decreased by 13.
c) The mannfacturing of laser printers produces 4% defective printers. Assume the chips
are independent and that a lot contains 1000 laser printers. Approxinate the probability that less than
35 printers are defective.
d) Suppose the random variables X and Y have the following joint probability mass function:
Xy f(x,y)
11 0.05
11 0.10
12 0.15
12 0.20
210.20
21 0.15
22 0.10
22 0.05
Find Conditional probability distribution of X given that Y = 1.
< o O

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