**Risk Taking and Investment Decisions**Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately **normally distributed** with a **mean** of 49 and a **standard deviation** of 16. The customers with scores in the bottom 10% are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to **one decimal place**. ---### Explanation of Terms:- **Normally Distributed:** This refers to a bell-shaped distribution that is symmetric about the mean, where most observations cluster around the central peak. The probability of occurrences are higher near the mean, decreasing as they move away.- **Mean:** The average score, which is 49 in this context.- **Standard Deviation:** This measures the spread of the data from the mean, which is 16 here. A higher deviation indicates more variability.- **Bottom 10% (Risk Averse):** These are the scores that fall in the lowest 10% of the normal distribution, indicating lower risk tolerance.### Calculation:To find the questionnaire score that distinguishes risk-averse customers, one would typically use the properties of the normal distribution, potentially using a z-score table or statistical software to determine the exact cutoff score at the 10th percentile.This task involves identifying the score below which 10% of the scores fall. This would be solved by calculating the z-score for the 10th percentile and then converting this z-score back to the original score scale using the mean and standard deviation provided.

Given X is normal Distributed with mean µ = 49.0 and standard deviation σ = 16.0 now will use…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 50.5 and a standard deviation of 16. The customers with scores in the bottom 5% are described as "risk averse. What is the questionnaire score that separates customers who are considered risk averse from those who ar not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. U Continue X S Submit Terms of Use | Privacy Center
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The picture is attached. If it is not clear, the shaded region of the graph represents 5%. Thanks in advance.
Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 49 and a standard deviation of 16 . The customers with scores in the bottom 15% are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

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