A telephone company’s goal is to have no more than six monthly line failures on any 100 kilometres of line. The company currently experiences an average of three monthly line failures per 50 kilometres of line. Let x denote the number of monthly line failures per 100 kilometres of line. Assuming x has a Poisson distribution:
a) Find the probability that the company will meet its goal on a particular 100 kilometres of line.
b) Find the probability that the company will not meet its goal on a particular 100 kilometres of line.
A company has three machines A, B and C which all produce the same two parts, X and
Y. of all the parts produced, machine A produces 60%, machine B produces 30%, and
machine C produces the rest. 40% of the parts made by machine A are part X, 50% of the
parts made by machine B are part X, and 70% of the parts made by machine C are part X.
A part produced by this company is randomly sampled and is determined to be an X part.
With the knowledge that it is an X part, find the probabilities that the part came from
machine A, B or C.
•statistics of business - Tofik, Sunday, April 24, 2016 at 3:50pm
A company has three machines A, B and C which all produce the same two parts, X and
Y. of all the parts produced, machine A produces 60%, machine B produces 30%, and
machine C produces the rest. 40% of the parts made by machine A are part X, 50% of the
parts made by machine B are part X, and 70% of the parts made by machine C are part X.
A part produced by this company is randomly sampled and is determined to be an X part.
With the knowledge that it is an X part, find the probabilities that the part came from
machine A, B or C.
To solve this problem, we need to use the Poisson distribution. The Poisson distribution is a probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average rate of events.
Let's solve these two parts step by step:
a) Find the probability that the company will meet its goal on a particular 100 kilometers of line.
We are given that the company currently experiences an average of three monthly line failures per 50 kilometers of line. This means the average rate of line failures per kilometer is lambda = (3 failures) / (50 kilometers) = 0.06 failures per kilometer.
To find the probability of meeting the goal of no more than six monthly line failures on 100 kilometers of line, we can calculate the cumulative probability of a Poisson distribution. In this case, we want to find P(X <= 6), where X is the number of monthly line failures per 100 kilometers of line.
Using a Poisson distribution table or a calculator, we can find that P(X <= 6) = 0.783.
Therefore, the probability that the company will meet its goal on a particular 100 kilometers of line is 0.783, or 78.3%.
b) Find the probability that the company will not meet its goal on a particular 100 kilometers of line.
To find the probability that the company will not meet its goal, we subtract the probability of meeting the goal from 1. In other words, P(not meeting the goal) = 1 - P(meeting the goal).
Using the result from part a), P(not meeting the goal) = 1 - 0.783 = 0.217.
Therefore, the probability that the company will not meet its goal on a particular 100 kilometers of line is 0.217, or 21.7%.