We consider a signal of intensity I, whose values can be modeled as a normal distribution with mean  and standard deviation  (both unknown). It is known that P(I < 12) = 0.9987 and P(I > 2) = 0.9720

(a) Obtain the values of  and . (b) Signals with intensity greater than 12 are classified as very high intensity. Determine the proportion of that type of emissions. (c) If in one session, the signal is emitted 20 times, what is the probability that a signal of very high intensity will be observed less than four times? (d) 3% of the signals, exceed what value?