Exercise 1: A company manufactures fuses whose service life can be approximated by a normal distribution having a mean of 1000 hours and a standard deviation of 200 hours. 1. What is the probability that a fuse will operate for more than 1330 hours? 2. The company would like to provide a replacement warranty for any fuse that does not exceed x0 hours of operation. Determine x0 if the company intends to replace a maximum of 2.5% of its fuses with this guarantee. 3. A sample of 10 fuses is taken at random and put into service in a process where they operate independently of each other. (a) Calculate the probability that at least 8 of the fuses in the sample fail after 1330 hours? (b) What is the probability that the average operating time of the 10 fuses in the sample is greater than 1100 hours?

Exercise 2: Suppose that the number of space debris hitting a satellite occurs according to a Poisson process with a rate of 3 per year. 1. What is the probability that no space debris will hit the satellite in a year? 2. What is the probability that there will be at least 3 impacts in 6 months? 3. The satellite goes into "diagnostic" mode after the fourth impact. A satellite is launched today, what is the probability that it will enter diagnostic mode for the first time during its second year of service?

Exercise 3: It is assumed that 78% of the seeds of a certain type of wheat germinate. If 340 seeds of this type of wheat are randomly selected, what is the probability that the proportion of seeds from this sample that will germinate is between 77.8% and 78.5%?