A salesperson goes door-to-door in a residential area to demonstrate the use of a new Household appliance to potential customers. She has found from her years of experience that after demonstration, the probability of purchase (long run average) is 0.30. To perform satisfactory on the job, the salesperson needs at least four orders this week. If she performs 15 demonstrations this week, what is the probability of her being satisfactory? What is the probability of between 4 and 8 (inclusive) orders?
Now the challenging questions: if the salesperson wants to be at least 90 percent confident of getting satisfactory evaluation in her job this week, how many demonstrations should she perform? How would your answers to above questions change if the probability of success increases (say by training) to 0.35?