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Suppose that a certain industrial process can be either in control or out of control; and that at any specified time the prior probability that it will be in control is 0.9 and the;: prior probability that it will be out of control is 0.1. A single observation X of the output of the process is to be taken, and it must be decided immediately whether the process is in control or out of control. If the process is in control. then X will have a normal distribution with mean 50 and variance 1. If the process is out of control, then X ill have a normal distribution with mean 52 and variance 1. If it is decided that the process is out of control when in fact it is in control, then the Joss from unnecessarily stopping the process will be $1000. If it is decided that the process is in control when in fact it is out of control, then the loss from continuing the process will be $18,000. If a correct decision is made, then the loss will be O. It is desired to find a test procedure for which the expected loss will be a minimum. For what values of X should it be decided that the process is out of control?
Newgroveton is a community of 445,000. In the most recent year, there were 750 new cases of disease A in the community.
An automobile assembly line operates for two shifts a day. The first shift accounts for two-thirds of the overall production.
Use these data to create a data-based CDF for the distribution of weights for lab animals. Estimate the probability that an animal's weight will be less than 9.5 grams.
A random sample of 8 petrol stations in each of three European countries A, B and C was taken. The price per litre at each station was recorded in Euros. The prices are given below.
What is the probability that a typical family will purchase and at least 3 tubes of toothpaste in any given month?
the power generated by a solar electric generator is normally distributed with mean 15.6 kilowatts and standard
A car rental company charges $50 a day and 20 cents per mile for renting a car. Let y be the total rental charges (in dollars) for a car for one day.
Two t-curves have degrees of freedom 12 and 20, respectively. Which one more closely resembles the standard normal curve? Explain your answer.
thickness measurements of a coating process are made to the nearest hundredth of a millimeter. the thickness
Hand Washing Ignaz Semmelweiss (1818-1865) was the doctor who first encouraged other doctors to wash their hands with disinfectant before touching patients.
If a new random sample of 50 newborns is taken from the same population, explain whether each of the following would change:- The population mean, μ.
He selects a sample of 100 women diagnosed with breast cancer in 2012, and finds that 93 were still alive in 2017.
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