Distributions - Some Questions

Probability distributions describe the possible outcomes of experiments. They are in some kind a universal description of the underlying random processes. In order to give a first impression, consider the questions below. The answers to the questions could be found easily if we knew the probability distributions of the involved processes.

• We flip a coin fifty times. How often will the head be up?
• We flip a coin again and again: When will the head be up the first time?
• We flip 20 coins at once for thirty times. Tell me more about the number of heads expected to be seen.
• Delta Motors Inc. produced 100,000 cars. 20,000 cars from this series are already sold to car-drivers, 80,000 cars are still at car dealers. Now technicians detect a mistake in construction. According to their calculation, 3% of the cars of this series will cause troubles during usage. The supervisory board of the company wants to know the probability of more than 1,000 cars showing this defect.
• A physicist baked a cake, mixing exactly 75 raisins into the dough. The cake is then cut into 8 equal pieces. Picking one piece, he counts 15 raisins in this piece of cake. Being very astonished about this fact (he expected 9 or 10 raisins), he wants to know the probability of finding 15 raisins  in this piece.
• The FBSPD (Federal Bureau of Statistics and Population Dynamics) is interested in the distribution of the body-height of the population (adults).
• Epsilon Insurance Inc. needs to calculate the risk of a client dying before his 60th birthday.
• What is the intensity of light in the center and at the border of a ground-glass screen?