At QT Sugar factory the amounts which go into bag of sugar are supposed to be normally distributed with mean 36 kg and standard deviation 0.1 kg. Once every 30 minutes a bag is selected from the production line, and its contents are noted precisely. If the amount of the bag goes below 35.8 kg or above 36.2 kg, then the bag will be declared out of control.If the process is in control, meaning p = 36 kg and o = 0.1 kg, find the probability that the bag will be declared out of control.In the situation of (a), find the probability that the number of bag found out of control in an eight-hour day (16 inspections) will be zero.In the situation of (a), find the probability that the number of bag found out control in an eight- hour day (16 inspections) will be exactly one.If the process shifts so that p =37 kg and o=0.4 kg find the probability that a bag will be declared out of control.

The mean of the distribution is 36 kg. The standard deviation of the distribution is 0.1 kg. The…

Answered: At QT Sugar factory the amounts which…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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At QT Sugar factory the amounts which go into bag of sugar are supposed to be normally distributed with mean 36 kg and standard deviation 0.1 kg. Once every 30 minutes a bag is selected from the production line, and its contents are noted precisely. If the amount of the bag goes below 35.8 kg or above 36.2 kg, then the bag will be declared out of control.

If the process is in control, meaning p = 36 kg and o = 0.1 kg, find the probability that the bag will be declared out of control.
In the situation of (a), find the probability that the number of bag found out of control in an eight-hour day (16 inspections) will be zero.
In the situation of (a), find the probability that the number of bag found out control in an eight- hour day (16 inspections) will be exactly one.
If the process shifts so that p =37 kg and o=0.4 kg find the probability that a bag will be declared out of control.

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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