Business Analytics
3rd Edition
ISBN: 9780135231678
Author: Evans, James R. (james Robert)
Publisher: PEARSON EDUCATION (COLLEGE)
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Chapter 4, Problem 1.45PE
To determine
Find the proportions of men and women in each profession.
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This problem is based on the fundamental option pricing formula for the continuous-time
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payoff F is given by:
We consider the two options below:
Fo=
-rT
= e
Eq[F].
1
A. An option with which you must buy a share of stock at expiration T = 1 for strike
price K = So.
B. An option with which you must buy a share of stock at expiration T = 1 for strike
price K given by
T
K =
T
St dt.
(Note that both options can have negative payoffs.) We use the continuous-time Black-
Scholes model to price these options. Assume that the interest rate on the money market
is r.
(a) Using the fundamental option pricing formula, find the price of option A. (Hint:
use the martingale properties developed in the lectures for the stock price process
in order to calculate the expectations.)
(b) Using the fundamental option pricing formula, find the price of option B.
(c) Assuming the interest rate is very small (r ~0), use Taylor…
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Chapter 4 Solutions
Business Analytics
Ch. 4 - Explain the science of statistics.Ch. 4 - What is a metric? How does it differ from a...Ch. 4 - Explain the difference between a discrete and a...Ch. 4 - Describe the four types of measurement scales and...Ch. 4 - What is a frequency distribution?Ch. 4 - Explain how to calculate a relative frequency.Ch. 4 - State how to use Excel for constructing frequency...Ch. 4 - State the features and limitations of the Excel...Ch. 4 - What does an ogive display?Ch. 4 - Prob. 2.6CYU
Ch. 4 - Prob. 3.1CYUCh. 4 - Prob. 3.2CYUCh. 4 - Prob. 3.3CYUCh. 4 - What is a cross-tabulation?Ch. 4 - Prob. 4.2CYUCh. 4 - Explain the difference between a population and a...Ch. 4 - List and explain the common measures of location...Ch. 4 - Prob. 5.3CYUCh. 4 - Prob. 5.4CYUCh. 4 - Prob. 5.5CYUCh. 4 - Prob. 5.6CYUCh. 4 - Prob. 5.7CYUCh. 4 - Prob. 5.8CYUCh. 4 - Prob. 6.1CYUCh. 4 - Use Excel to find the mean and variance for the...Ch. 4 - Prob. 7.1CYUCh. 4 - Prob. 7.2CYUCh. 4 - Prob. 8.1CYUCh. 4 - Prob. 8.2CYUCh. 4 - Prob. 9.1CYUCh. 4 - Prob. 9.2CYUCh. 4 - Prob. 9.3CYUCh. 4 - What rules are typically used to identify...Ch. 4 - Prob. 10.2CYUCh. 4 - Summarize statistical tools that are typically...Ch. 4 - Prob. 11.2CYUCh. 4 - What are the principles of statistical thinking?Ch. 4 - Prob. 12.2CYUCh. 4 - Prob. 12.3CYUCh. 4 - A survey handed out to individuals at a major...Ch. 4 - Prob. 1.2PECh. 4 - Identify each of the variables in the Excel file...Ch. 4 - Prob. 1.4PECh. 4 - Prob. 1.5PECh. 4 - Prob. 1.6PECh. 4 - Prob. 1.7PECh. 4 - Prob. 1.8PECh. 4 - Prob. 1.9PECh. 4 - Prob. 1.10PECh. 4 - Prob. 1.11PECh. 4 - Prob. 1.12PECh. 4 - Use a PivotTable to construct a frequency...Ch. 4 - Prob. 1.14PECh. 4 - Prob. 1.15PECh. 4 - Prob. 1.16PECh. 4 - Prob. 1.17PECh. 4 - Prob. 1.18PECh. 4 - Prob. 1.19PECh. 4 - Prob. 1.20PECh. 4 - Use a PivotTable to construct a cross-tabulation...Ch. 4 - Use PivotTables to construct cross-tabulations for...Ch. 4 - Prob. 1.23PECh. 4 - Prob. 1.24PECh. 4 - Prob. 1.25PECh. 4 - Compute the mean, median, midrange, and mode for...Ch. 4 - Considering the data in the Excel file Home Market...Ch. 4 - Considering the data in the Excel file Home Market...Ch. 4 - In the Excel file Facebook Survey, find the range,...Ch. 4 - Prob. 1.30PECh. 4 - For the Excel file Tablet Computer Sales, find the...Ch. 4 - The Excel file Atlanta Airline Data provides...Ch. 4 - Prob. 1.33PECh. 4 - Prob. 1.34PECh. 4 - Apply the Descriptive Statistics tool for subsets...Ch. 4 - Use the Descriptive Statistics tool to summarize...Ch. 4 - Prob. 1.38PECh. 4 - The Data worksheet in the Excel file Airport...Ch. 4 - Prob. 1.40PECh. 4 - Prob. 1.41PECh. 4 - Prob. 1.42PECh. 4 - Prob. 1.43PECh. 4 - Prob. 1.44PECh. 4 - Prob. 1.45PECh. 4 - Prob. 1.46PECh. 4 - Prob. 1.47PECh. 4 - Prob. 1.48PECh. 4 - Prob. 1.49PECh. 4 - Prob. 1.50PECh. 4 - Prob. 1.51PECh. 4 - Prob. 1.52PECh. 4 - Prob. 1.53PECh. 4 - In the Excel file Debt and Retirement Savings, use...Ch. 4 - Prob. 1.55PECh. 4 - Prob. 1.56PECh. 4 - Prob. 1.57PECh. 4 - Prob. 1.58PECh. 4 - Prob. 1.59PECh. 4 - In the Excel file Weddings, determine the...Ch. 4 - Prob. 1.61PECh. 4 - The Excel file Beverage Sales lists a sample of...Ch. 4 - For the Presidents Inn Guest Database, find the...Ch. 4 - Prob. 1.64PECh. 4 - For the Excel file Credit Risk Data, compute the...Ch. 4 - Compute the z-scores for the data in the Excel...Ch. 4 - Prob. 1.67PECh. 4 - In the Excel file Weddings, find the mean, median,...Ch. 4 - Use the following approaches to analyze the survey...Ch. 4 - Prob. 1.70PECh. 4 - A producer of computer-aided design software for...Ch. 4 - Prob. 1.72PECh. 4 - Prob. 1.73PECh. 4 - A Midwest pharmaceutical company manufactures...Ch. 4 - Find the mean and variance of a deck of 52 cards,...Ch. 4 - Elizabeth Burke has received several questions...
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- Review a classmate's Main Post. 1. State if you agree or disagree with the choices made for additional analysis that can be done beyond the frequency table. 2. Choose a measure of central tendency (mean, median, mode) that you would like to compute with the data beyond the frequency table. Complete either a or b below. a. Explain how that analysis can help you understand the data better. b. If you are currently unable to do that analysis, what do you think you could do to make it possible? If you do not think you can do anything, explain why it is not possible.arrow_forward0|0|0|0 - Consider the time series X₁ and Y₁ = (I – B)² (I – B³)Xt. What transformations were performed on Xt to obtain Yt? seasonal difference of order 2 simple difference of order 5 seasonal difference of order 1 seasonal difference of order 5 simple difference of order 2arrow_forwardCalculate the 90% confidence interval for the population mean difference using the data in the attached image. I need to see where I went wrong.arrow_forward
- Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADOarrow_forwardSuppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?arrow_forwardA normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forward
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- In order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forwardProblem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…arrow_forward
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