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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. a) If the process is in control, meaning u = 36 kg and o= 0.1 kg, find the probability that the bag will be declared out of control. b) 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. c) 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. d) 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.

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. a) If the process is in control, meaning u = 36 kg and o= 0.1 kg, find the probability that the bag will be declared out of control. b) 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. c) 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. d) 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.

A First Course in Probability (10th Edition)
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. a) If the process is in control, meaning u= 36 kg and o= = 0.1 kg, find the probability that the bag %3D will be declared out of control. b) 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. c) 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. d) If the process shifts so that u =37 kg and o=0.4 kg find the probability that a bag will be declared out of control.
Transcribed Image Text: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. a) If the process is in control, meaning u= 36 kg and o= = 0.1 kg, find the probability that the bag %3D will be declared out of control. b) 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. c) 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. d) If the process shifts so that u =37 kg and o=0.4 kg find the probability that a bag will be declared out of control.
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