Question

A system has a large number of components of the same type. Assume that the failure time T (measured in hours) of any of these components follows approximately a normal distribution, with mean 100 and standard deviation 20. Using this approximation, answer the following questions. a) To obtain the probability that a randomly selected component lasts more than 115 hours, the standardized value is Z= ? ; thus, the probability sought is: ? b) It is desired to give a replacement warranty for any component that lasts less than M hours. Find the value of M so that the probability of the warranty being honored is only 3%. c) If a random sample of 80 components of the same type is selected, what is the mean expected sample failure time : and its standard deviation. standard deviation . The probability that the sample mean time is at least 98 hours would be:

Name: a system has a large number of components of the same type assume that the failure time t measured in hours of any of these components follows approximately a normal distribution with mean 1 79183
Uploaded: 2023-06-01T19:28:02-08:00
Duration: 2 min 39 s
Channel: Numerade
Description: a system has a large number of components of the same type assume that the failure time t measured in hours of any of these components follows approximately a normal distribution with mean 1 79183

          A system has a large number of components of the same type.
Assume that the failure time T (measured in hours) of any of these
components follows approximately a normal distribution, with mean
100 and standard deviation 20. Using this approximation, answer the
following questions. 
a) To obtain the probability that a randomly selected component
lasts more than 115 hours, the standardized value is Z= ? ; thus,
the probability sought is: ?
b) It is desired to give a replacement warranty for any
component that lasts less than M hours. Find the value of M so that
the probability of the warranty being honored is only
3%. 
c) If a random sample of 80 components of the same type is
selected, what is the mean expected sample failure time : and its
standard deviation. 
standard deviation 
. The probability that the sample mean time is at least 98 hours
would be:

Added by Matthew B.

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