6 A company owns two machines, \(A\) and \(B\), which make toys. Both machines run continuously and independently.
Machine \(A\) makes an average of 2 errors per hour.
6
- Using a Poisson model, find the probability that the machine makes exactly 5 errors in 4 hours, giving your answer to three significant figures.
6
- Machine \(B\) makes an average of 5 errors per hour. Both machines are switched on and run for 1 hour.
The company finds the probability that the total number of errors made by machines \(A\) and \(B\) in 1 hour is greater than 8 .
If the probability is greater than 0.4 , a new machine will be purchased.
Using a Poisson model, determine whether or not the toy company will purchase a new machine.
6 - After investigation, the standard deviation of errors made by machine \(A\) is found to be 0.5 errors per hour and the standard deviation of errors made by machine \(B\) is also found to be 0.5 errors per hour.
Explain whether or not the use of Poisson models in parts (a) and (b) is appropriate.