You are a production manager in a factory. A key machine on the production line is blowing fuses at an average rate of 27 per week. Blown fuses seems to occur at random at a fairly constant rate throughout the week. You have decided to install a voltage regulator on this machine. (Show workings)

1. Assuming that the voltage regulator has no effect, what distribution best describes the number of fuses blown during a week? Give all relevant parameters.
2. Determine the mean and standard deviation of the number of fuses blown per week.
3. After the voltage regulator is installed the machine blows 23 fuses during the subsequent week. If the underlying rate hasn't actually changed (i.e. the voltage regulator have no effect on fuses blowing) how likely is it to get 23 or fewer blown fuses in a week? (NB you may attempt this problem using a Normal approximation OR by using Excel to determine an exact probability.)
4. Assuming that there is some cost associated with installing the voltage regulator, do you think it would be worthwhile to make the change permanent? [Note, the value you calculated in part (3) is known as a p-value, it should be useful in guiding your decision].