A discharge (or response) rate of auditory nerve fibers [recorded as the number of spikes per 200 milliseconds (ms) of noise burst] is used to measure the effect of acoustic stimuli in the auditory nerve. An empirical study of auditory nerve fiber response rates in cats resulted in a mean of 15 spikes/ms (Journal of the Acoustic-cal Society of America, Feb. 1986). Let Y represent the auditory nerve fiber response rate for a randomly selected cat in the study.

a. If Y is approximately a Poisson random variable, find the mean and standard deviation of Y.

b. Assuming Y is Poisson, what is the approximate probability that Y exceeds 27 spikes/ms? 

c. In the study, the variance of Y was found to be “substantially smaller” than 15 spikes/ms. Is it reasonable to expect Y to follow a Poisson process? How will this affect the probability computed in part b?