(30 points) 2. An analog signal can be received at a detector from two sources A and B. If the signal is received from source A, it follows a Normal distribution with mean 100 and a variance of 256. If the signal is received from source B, it follows a Normal distribution with mean 150 and variance 260. The signal is received from source A 40% of the time. What is the probability that the signal will be less than 120 microvolts? Solve the problem mathematically (by converting each to standard Normal distribution and conditional probability). Also, write R code to compute the probability.