The firing rates of 100 neurons are recorded in a particular region of the brain of a monkey under each of two experimental conditions. The number of neurons in which the firing rate is greater in Condition 1 than in Condition 2 is counted. Suppose that in the population of neurons the probability of a higher firing rate for Condition 1 is 0.58.
a) What is the probability that exactly 90 out of the 100 have higher firing rates for Condition 1? (binomial distribution)
b) What is the probability that at least 40 but no more than 60 neurons have higher firing rates for Condition 1? (40<=x<60)
c) What is the number of neurons n such that the probability of more than n neurons have higher firing rates for Condition 1is 0.99?