1. Find the equation of the multiple regression plane of Z on X and Y from the following data. X: 30 40 20 Y: 50 60 40 20 60 11 10 7 15 19 12 8 14 Z: 110 80 70 120 150 90 70 120 2. It has been established that the number of defective stereos produced daily at a certain plant is Poisson distributed with mean 4. Over a 2 days span, what is the probability that the number of defective stereos does not exceed 3? 3. The amount of time that a watch will run without having to be reset is a random variable having an exponential distribution with mean 120 days. Find the probability that such a watch will (i). have to be set in less than 24 days, and (ii). not have to be reset in at least 180 days. 4. The marks obtained by a number of students in a certain subject are assumed to be approximately normally distributed with mean 55 and a SD of 5. If 5 students are taken at random from this set, then what is the probability that 3 of them would have scored marks above 60? 5. Write the Detailed Report on Applications of Probability Distributions or Sampling Techniques in Science, Engineering, or Technology Oriented Problems for minimum 1 page. **********