1.Sam and Alex are arguing about probability.Sam thinks that he can figure out the probability of a certain event's outcomes occurring by observing and recording the results, and then using those results to create the probability.Alex believes she can create a model of the event and its outcomes, and thus calculate the probability.

a.What kind of probability is Sam using?

b.What kind of probability is Alex using?

c.How could Sam prove to Alex that his calculation is correct?What theorem would he be using?

d.A third friend, Jordan, says that they can just go ahead and state the probability because they have a "feeling".What kind of probability is this?

2.Suppose we have a bag of 20 marbles.4 are blue, 5 are purple, 3 are green and the rest are yellow. Round your answer to three decimal places.Please show all work, including any formulas or explanations of what numbers you are using.

a.Construct a probability model.

b.How did you figure out the probability for the yellow marbles?

c.With replacement, what is the probability that first you draw a red marble, and then a yellow marble?

d.Without replacement, what is the probability that first you draw a yellow marble and then another yellow marble?

3.Using the model from 2, suppose we define p as the probability of getting a purple marble.Suppose there are 10 trials of picking a marble.Using the binomial probability, answer the following questions. Show all work, including calculator commands.Round your answer to three decimal places.

a.What is the probability that half of the marbles selected will be purple?

b.What is the probability that at most 7 purple marbles will be selected?

c.What is the probability that 5 or more will be selected?

4.For the following question, make sure you draw the normal curve, indicate the mean and observation(s) and shade the appropriate area.Include your work and calculator commands.Round your answer to four decimal places.

The Boeing 757-200 ER airliner carries 200 passengers and has door with a height of 72 inches.Heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.

a.If a male passenger is selected, find the probability that he can fit through the door without bending.

b.If half of the 200 passengers are men, find the probability that the sample mean height of the 100 men are less than 72 inches.

c.When considering the comfort and safety of passengers, which result is more relevant?The probability from part a or part b.Why?

d.When considering the comfort and safety of passengers, why are women ignored in this case?