### Economic Conditions and Standard Deviation of ReturnsCarson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. #### Question:What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations.#### Economic Conditions Probability Distribution:| **Economic Conditions** | **Prob.** | **Return** ||--------------------------|-----------|------------|| Strong | 30% | 27.0% || Normal | 40% | 13.0% || Weak | 30% | -17.0% |#### Answer Choices:- a. 17.49%- b. 12.36%- c. 22.49%- d. 10.10%- e. 18.36%#### Explanation:To find the standard deviation of the returns, we use the formula for standard deviation of a population. Here are the steps:1. **Calculate the Expected Return (Mean)**:\[ E(R) = \sum (P_i \times R_i) \]Where $ P_i $ is the probability of each economic condition, and $ R_i $ is the return.2. **Compute the Variance**:\[ \sigma^2 = \sum [P_i \times (R_i - E(R))^2] \]3. **Find the Standard Deviation**:\[ \sigma = \sqrt{\sigma^2} \]Use these steps to calculate the actual standard deviation based on the given probabilities and returns.----------This problem illustrates the concept of standard deviation in the context of varying economic conditions and expected returns, a crucial topic in financial management and investment analysis. Understanding how to calculate and interpret standard deviation helps in assessing risk and making better-informed financial decisions.

The standard deviation of a portfolio measures how much the investment returns deviate from the mean…

Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations. Economic Conditions Strong Normal Weak O a. 17.49% O b. 12.36% O c. 22.49% O d. 10.10% O e. 18.36% Prob. 30% 40% 30% Return 27.0% 13.0% -17.0%

Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations. Economic Conditions Strong Normal Weak O a. 17.49% O b. 12.36% O c. 22.49% O d. 10.10% O e. 18.36% Prob. 30% 40% 30% Return 27.0% 13.0% -17.0%

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter8: Time Series Analysis And_forecasting

Section: Chapter Questions

Problem 22P: Consider the following time series: a. Construct a time series plot. What type of pattern exists in...

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