Your dog Toto is prone to uncontrollable fits of barking. Currently he barks on average 54 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 Squeaky toy that claims to have calming properties, as the pet store has offered you a free trial of the toy. a) [2 marks] Assuming that the squeaky toy has no effect, what distribution best describes the number of times Toto will bark during the day? Give all relevant parameters. b) [2 marks] Determine the mean and standard deviation of the number of barks per day. c) [3 marks] The first day with the new toy Toto barks just 37 times. If the underlying rate of barking fits hasn't actually changed (i.e. the new toy has 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.) d) [2 marks] Assuming that the new toy is not cheap, explain whether you think it would be worthwhile to keep the new toy or return it to the shop? [Note, the value you calculated in part (c) is known as a p-value, it should be useful in guiding your decision].