Suppose that the time between failures, Ti, is approximately normally distributed with mean400 hours and variance 10,000. The repair time of the equipment is also approximately normally distributed with mean 10 hours and variance 11.6. Find the probability that there aremore than six repair cycles within a one-year period. Assume that one year corresponds to2,000 hours of operation.
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.
Suppose that the time between failures, Ti
, is approximately
400 hours and variance 10,000. The repair time of the equipment is also approximately normally distributed with mean 10 hours and variance 11.6. Find the
more than six repair cycles within a one-year period. Assume that one year corresponds to
2,000 hours of operation.
We can use the normal distribution to model the number of repair cycles in a one-year period.
First, we need to find the mean and variance of the number of repair cycles in a 2,000 hour period. Since the repair time is approximately normally distributed with mean 10 and variance 11.6, the mean repair time for a 2,000 hour period is:
2,000 / 10 = 200
Similarly, since the time between failures is approximately normally distributed with mean 400 and variance 10,000, the number of failures in a 2,000 hour period is:
2,000 / 400 = 5
Therefore, the number of repair cycles in a 2,000 hour period is the minimum of 5 and the number of times the equipment fails in that period.
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