Your dog Jasper is prone to uncontrollable fits of barking. Currently he barks on average 53 times per day. Barking seems to occur at random at a fairly constant rate throughout the day. You have decided to trial giving him a breakfast kibble that claims to have calming properties.

1. [2 marks] Assuming that the new kibbles have no effect, what distribution best describes the number of times Jasper will bark during the day? Give all relevant parameters.
2. [2 marks] Determine the mean and standard deviation of the number of barks per day.
3. [3 marks] The first day on the new kibble Jasper barks just 37 times. If the underlying rate of barking fits hasn't actually changed (i.e. the new kibbles have no effect on barking) how likely is it to get 37 or fewer barking fits? (NB you may attempt this problem using a Normal approximation OR by using Excel to determine an exact probability.)
4. [2 marks] Assuming that the new kibbles are a bit more expensive than the old kibbles, do you think it would be worthwhile to make the change permanent? [Note, the value you calculated in part (c) is known as a p-value, it should be useful in guiding your decision].