Answer each between 150-200 words.

-In §4.4 we are introduced to the concept of conditional probability. The notation P(A | B) denotes the probability of event A occurring given that we know event B has occurred.

Now consider the Monty Hall Problem introduced in the following video:

• After watching this video, we know that if we are given the option to switch doors that, probabilistically speaking, it is in our best interest to switch.
• Explain why this is the case using your knowledge of conditional probability.

-In §6.2 we are introduced to the Normal Probability Distribution and the special case of the Normal Probability Distribution, the Standard Normal Probability Distribution, which is a Normal Probability Distribution with mean (u) zero and variance (σ2) one.

One way to find probabilities from a Standard Normal Distribution is to use probability tables, which are located inside the front cover of your textbook.

• According to the table, what is the probability when z ≤ -1.75? The probability when z ≤ 1.75?
• What properties of probability distributions and specifically the Normal Probability Distribution do you notice from the two probabilities that you have found in the table?

-Go to the link: http://www.random.org/dice/

• Roll the 2 virtual dice and calculate the sum of the pair of virtual dice. Do this 10 times.
• Then after you have rolled the virtual pair dice 10 times and calculated 10 sums calculate the average of these 10 sums.
• Conduct this experiment again but this time roll the virtual pair of dice 20 times and calculate the 20 sums and then find the average of these 20 sums.
• Post your results and discussion how this relates to this week’s lesson, particularly the Central Limit Theorem.

-In the discussion for week 4, you rolled a pair of dice 10 times and calculated the average sum of your rolls.

• Then you did the same thing with 20 rolls.
• Use your results from the week 4 discussion for the average of 10 rolls and for the average of 20 rolls to construct a confidence interval for the true mean of the sum of a pair of dice (assume σ = 2.41).
• What do you notice about the length of the interval for the mean of 10 rolls versus the mean of 20 rolls? Did you expect this? Why or why not?

-In §9.2 the concepts of Type I and Type II errors are introduced.

• Now consider the situation where a husband and wife go to the doctor’s office to each get some tests run and the doctor accidently mixes up their charts. The doctor comes into the exam room with the results of the tests and declares that the wife is NOT pregnant but her husband IS indeed pregnant with a baby.
• How does this illustrate the concepts behind Type I and Type II errors?
• With this situation in mind, what type of error (Type I or Type II) is worse? Explain your reasoning.

-Using the given Height and Weight data set, follow the steps in the weekly video or on pages 584-585 of the textbook for performing a regression analysis using Excel to analyze the Height and Weight Data set (assume height is the input variable x and weight is the output variable y).

• Once you have performed the analysis in Excel, state the correct simple linear regression equation and use the regression equation to predict the weight (in pounds) of a person who is 65 inches tall and the weight (in pounds) of a person who is 100 inches tall.
• Why might the regression equation you have found not be a good predication of the weight of someone who is 100 inches tall?

Download the Height and Weight Table Here.

-When you started the course you may have known some basic principles but now you have a solid foundation to tackle many different problems.

Please answer the following questions:

• Did the course meet your expectations?
• How do you feel about your progress in the course? Are you surprised with your progress?
• What is one concept that you wish you understood better?
• What advice would you give to a student starting the class next term?