Category: Exams

For the final exam, you should complete 10 exercises in the “Final Exam Exercises” WebWork set, and also submit the following written solutions and spreadsheet calculations.

The WebWork exercises and your written solutions (& spreadsheet link) are due Friday at 5pm. Good luck!

#1: Write down your calculation for “The percentage of students with over X dollars in their possession” (in terms of the frequencies shown on the histogram and the sample size n).

#2: Calculate the regression parameters in a spreadsheet. Write out the calculation of the predicted value in your written solutions.

#3: Write out each probability as a ratio of two integers, and use the “P(event)” notation.

#4: For each of the probabilities you are asked for, write down the set of outcomes in the event.

#5: Write down P(A), P(B), and P(A and B) (using the given information), and then write out the calculations of  conditional probabilities asked for in the exercise (using the definition of conditional probability).

#6: Write down the calculation of the size of the sample space for this probability experiment (of choosing a committee of four at random from this group of people).  Then write down the calculations of the following probabilities: (a) the committee consists of all women, and (b) the committee contains at least one man. (Hint: See Exam #3, Exercise #1.)

#7: Write down the probability distribution for the random variable X = “your net win/loss in this raffle” and write out your calculation of the expected value E[X].  (Note: WebWork requires you to include “$” in your typed solution for this exercise, and if you find the expected value is negative, include a negative sign before the dollar sign. For example, to enter an expected value of negative 50 cents, enter “-$0.50”)

#8: Write out the calculation of the expected value.

#9: Write down the values of n, p, and q for this binomial experiment.  Write down the calculations of the expected value and standard deviation. (Hint: use the formulas given on the class outline and on Exam #3.)

Calculate the entire binomial probability distribution for this binomial random variable in your spreadsheet (using the spreadsheet function =binomdist(i, n, p, false)).  Use  your spreadsheet to calculate the probability asked for in the exercise.

#10: Sketch the normal distribution curve with the given mean and standard deviation (see the last class outline!). Indicate on your sketch the areas under the curve corresponding to the probabilities asked for in the exercise, using the notation “P(X < c)” or “P(X > c)” for each.

Finally, calculate the given probabilities in your spreadsheet (using the spreadsheet function “=normdist(c, mean, stddev, true” which outputs P(X < c)) .

You can ignore part (c) for this exercise!

A reminder that Exam #3 is available in Files, and is a take-home exam due Monday night (May 18).  Here is an outline that may help you approach the exercises on the exam:

• #1: parts (a) and (b) are combinations calculations; you should write out these calculations in detail (see for example the solutions to HW8). Part (c) is a probability calculation which uses the results from (a) and (b), and (d) uses the result from (c).  (The probability experiment in this exercise is randomly choosing 3 children from the class of 10 children; in (c) and (d) you are calculating the probabilities of the given events for this probability experiment.)
• #2: for part (a) compute the relative frequencies, and in part (b) graph them as a histogram.  Part (c) involves calculating probabilities, assuming we interpret the relative frequencies as probabilities; see HW9-RandomVariables: Problem 2 for a similar example.
• #3: This is all about a binomial experiment/random variable, so review the class outline on that topic. In particular, review the definition of a binomial experiment, and refer to it to write out the explanation for part (b).  For the table in part (c), it may help to review the Google spreadsheet we set up in class yesterday (Binomial Distribution Calculation), and to set up a similar one to help you fill out the table.  For part (d), use the formulas that are given right there on the exam!
• #4: Parts (a) and (b) are similar to some of the exercises on HW9-RandomVariables (see Problems 2, 3, 5, 6). For part (c), use the definition of expected value E[X] which we covered on the class outline, and was also on Exam #2 (#2(b)).
• #5: For (b), again refer to the definition of a binomial experiment for your explanation (as in #3(b)); and for (c), use the formula for expected value of a binomial random variable (as given in #3(d)!). For (d), again refer to the Binomial Distribution Calculation spreadsheet we set up in class.
  • But note that, as I said on the exam, you can just use the spreadsheet command =binomdist(i,n,p,false) to generate the binomial probability distribution of X, i.e., you don’t need to implement the entire binomial distribution formula, as we did in the shared spreadsheet.
  • As with Exam #2, please submit the link to your spreadsheet for #5(d) along with your written solutions for the exam.