Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Chapter 15.1, Problem 10P
Carter has a large collection of marbles. He knows that he has exactly 20 blue marbles in his collection, but he does not know how many marbles he has in all. Carter mixes up his marbles and randomly picks out 40 marbles. Of the 40 marbles he picked, four are blue. Based on these results, what is the best estimate you can give for the total number of marbles in Carter’s collection? Explain your reasoning. Solve this problem in three different ways, explaining your reasoning in each case.
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Chapter 15 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 15.1 - Give two examples of a statistical question and...Ch. 15.1 - A class has a collection of 100 bottle caps and...Ch. 15.1 - Neil, a third-grader, asked 10 of his classmates...Ch. 15.1 - An announcer of a TV program invited viewers to...Ch. 15.1 - There is a bowl containing 300 plastic tiles. Some...Ch. 15.1 - There is a bowl containing 80 green tiles and an...Ch. 15.1 - At a factory that produces doorknobs, 1500...Ch. 15.1 - At a factory that produces switches, 3000 switches...Ch. 15.1 - At a light bulb factory, 1728 light bulbs are...Ch. 15.1 - Carter has a large collection of marbles. He knows...
Ch. 15.1 - The following problem is an example of the...Ch. 15.1 - A group studying violence wants to determine the...Ch. 15.2 - Three third-grade classes are having a contest to...Ch. 15.2 - Find 3 coins of any type (as long as all 3 have a...Ch. 15.2 - Table 15.3 shows women’s 400-meter freestyle...Ch. 15.2 - Using an Internet browser, go to census.gov, the...Ch. 15.2 - Using an Internet browser, go to the webpage of...Ch. 15.2 - Using an Internet browser, go to one of the...Ch. 15.2 - Using an Internet browser, go to one of the...Ch. 15.2 - a. Describe in detail an activity suitable for use...Ch. 15.3 - In your own words, explain why the following two...Ch. 15.3 - Explain why the mean of a list of numbers must...Ch. 15.3 - Explain why the mean of two numbers is exactly...Ch. 15.3 - Shante caught 17 ladybugs every day for 4 days....Ch. 15.3 - John’s average annual income over a 4-year period...Ch. 15.3 - Tracy’s times swimming 200 yards were as follows:...Ch. 15.3 - Explain how you can quickly calculate the mean of...Ch. 15.3 - Explain how you can quickly calculate the mean of...Ch. 15.3 - average on her first 3 math tests was 80. Her...Ch. 15.3 - A teacher gives a 10-point test to a class of 10...Ch. 15.3 - In your own words, describe how to view the mean...Ch. 15.3 - Discuss Jessica’s reasoning about calculating the...Ch. 15.3 - ]The dot plot in Figure 15.21 represents the...Ch. 15.3 - For each of the following situations, decide...Ch. 15.3 - A teacher gives a 10-point test to a class of 9...Ch. 15.3 - A teacher gives a 10-point test to a class of 9...Ch. 15.3 - In Ritzy County, the average annual household...Ch. 15.3 - In county A, the average score on the grade 5 Iowa...Ch. 15.3 - a. The histogram at the top of Figure 15.22 shows...Ch. 15.3 - * Ms. Smith needs to figure her students’ homework...Ch. 15.3 - The average speed of a moving object during a...Ch. 15.4 - What is the difference between scoring in the 90th...Ch. 15.4 - What is the purpose of reporting a student’s...Ch. 15.4 - The three histograms in Figure 15.37 show the...Ch. 15.4 - At a math center in a class, there is a bag filled...Ch. 15.4 - Refer to Figure 15.26 on page 706. a. Refer to the...Ch. 15.4 - Refer to Figure 15.26 on page 706. a. Refer to the...Ch. 15.4 - Refer to Figure 15.26 on page 706. a. Write at...Ch. 15.4 - Use the NAEP long-term trend data about...Ch. 15.4 - Determine the median and interquartile range for...Ch. 15.4 - a. Make a box plot for the data in Figure 15.38....Ch. 15.4 - Determine the medians and interquartile ranges for...Ch. 15.4 - a. Make box plots for the dot plots in Figure...Ch. 15.4 - A fifth-grade class is wondering ¡f girls’ names...Ch. 15.4 - Compute the mean and the MAD for each of the dot...Ch. 15.4 - On a state-wide test graded on a 10-point scale,...Ch. 15.4 - A 400-point test is given to a group of students....
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- Question 2. An American option on a stock has payoff given by F = f(St) when it is exercised at time t. We know that the function f is convex. A person claims that because of convexity, it is optimal to exercise at expiration T. Do you agree with them?arrow_forwardQuestion 4. We consider a CRR model with So == 5 and up and down factors u = 1.03 and d = 0.96. We consider the interest rate r = 4% (over one period). Is this a suitable CRR model? (Explain your answer.)arrow_forwardQuestion 3. We want to price a put option with strike price K and expiration T. Two financial advisors estimate the parameters with two different statistical methods: they obtain the same return rate μ, the same volatility σ, but the first advisor has interest r₁ and the second advisor has interest rate r2 (r1>r2). They both use a CRR model with the same number of periods to price the option. Which advisor will get the larger price? (Explain your answer.)arrow_forward
- Question 5. We consider a put option with strike price K and expiration T. This option is priced using a 1-period CRR model. We consider r > 0, and σ > 0 very large. What is the approximate price of the option? In other words, what is the limit of the price of the option as σ∞. (Briefly justify your answer.)arrow_forwardQuestion 6. You collect daily data for the stock of a company Z over the past 4 months (i.e. 80 days) and calculate the log-returns (yk)/(-1. You want to build a CRR model for the evolution of the stock. The expected value and standard deviation of the log-returns are y = 0.06 and Sy 0.1. The money market interest rate is r = 0.04. Determine the risk-neutral probability of the model.arrow_forwardSeveral markets (Japan, Switzerland) introduced negative interest rates on their money market. In this problem, we will consider an annual interest rate r < 0. We consider a stock modeled by an N-period CRR model where each period is 1 year (At = 1) and the up and down factors are u and d. (a) We consider an American put option with strike price K and expiration T. Prove that if <0, the optimal strategy is to wait until expiration T to exercise.arrow_forward
- We consider an N-period CRR model where each period is 1 year (At = 1), the up factor is u = 0.1, the down factor is d = e−0.3 and r = 0. We remind you that in the CRR model, the stock price at time tn is modeled (under P) by Sta = So exp (μtn + σ√AtZn), where (Zn) is a simple symmetric random walk. (a) Find the parameters μ and σ for the CRR model described above. (b) Find P Ste So 55/50 € > 1). StN (c) Find lim P 804-N (d) Determine q. (You can use e- 1 x.) Ste (e) Find Q So (f) Find lim Q 004-N StN Soarrow_forwardIn this problem, we consider a 3-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year. The interest rate is r = 0%. 16 22 28 12 16 12 8 4 2 time Figure 1: Stock evolution for Problem 1. (a) A colleague notices that in the model above, a movement up-down leads to the same value as a movement down-up. He concludes that the model is a CRR model. Is your colleague correct? (Explain your answer.) (b) We consider a European put with strike price K = 10 and expiration T = 3 years. Find the price of this option at time 0. Provide the replicating portfolio for the first period. (c) In addition to the call above, we also consider a European call with strike price K = 10 and expiration T = 3 years. Which one has the highest price? (It is not necessary to provide the price of the call.) (d) We now assume a yearly interest rate r = 25%. We consider a Bermudan put option with strike price K = 10. It works like a standard put, but you can exercise it…arrow_forwardIn this problem, we consider a 2-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year (At = 1). The yearly interest rate is r = 1/3 = 33%. This model is a CRR model. 25 15 9 10 6 4 time Figure 1: Stock evolution for Problem 1. (a) Find the values of up and down factors u and d, and the risk-neutral probability q. (b) We consider a European put with strike price K the price of this option at time 0. == 16 and expiration T = 2 years. Find (c) Provide the number of shares of stock that the replicating portfolio contains at each pos- sible position. (d) You find this option available on the market for $2. What do you do? (Short answer.) (e) We consider an American put with strike price K = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe the optimal exercising strategy. (f) We consider an American call with strike price K ○ = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe…arrow_forward
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