Questions: 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 14. 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.

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 14. 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.
Transcript text: 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 14. 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.
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Z-Score for the 15th Percentile

To find the z-score corresponding to the 15th percentile, we use the formula for the z-score:

\[ z = \frac{X - \mu}{\sigma} \]

For the 15th percentile, we have:

\[ z = \frac{0.15 - 0}{1} = 0.15 \]

Thus, the z-score for the 15th percentile is:

\[ z = 0.15 \]

Step 2: Convert the Z-Score to the Questionnaire Score

Next, we convert the z-score to the actual questionnaire score using the mean (\(\mu = 50.5\)) and standard deviation (\(\sigma = 14\)):

\[ X = \mu + z \cdot \sigma \]

Substituting the values:

\[ X = 50.5 + 0.15 \cdot 14 \]

Calculating this gives:

\[ X = 50.5 + 2.1 = 52.6 \]

Final Answer

The questionnaire score that separates customers who are considered risk averse from those who are not is:

\[ \boxed{52.6} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Identify the characteristics of progressive corporate cultures that give them an advantage over traditional compliance-based cultures. (Check all that apply) They focus solely on meeting legal requirements. They have a more stable bottom line. They minimize all risks. They are sustainable.
failedAnswered
Dr. Bogdarian noticed that one of her students addresses her with the word mother instead of the word professor or doctor. Dr. Bogdarian applies the principles of (hint: Freud), and hypothesizes the student misspeaks because he is unconsciously associating her with his mother. functionalism Gestalt psychology psychoanalytic (psychodynamic) theory structuralism
failedAnswered
Order the items from most general to most specific. most general William Shakespeare playwright writer most specific
failedAnswered
1. The Koran was written by Muhammad in Arabic and became the cornerstone of Islam. True or False? a. True b. False 2. Jerusalem was only a holy site for those of Jewish faith. True or False? a. True b. False 3. The Inquisition was a peaceful attempt to spread Christianity under King Ferdinand and Queen Isabella. True or False? a. True b. False
failedAnswered
Responde las preguntas 1 y 2 de acuerdo con la siguiente información. Se tienen dos tanques llenos con agua con una densidad de 1000 Kg / m^3, uno de un área de 55 m^2 y el otro de un área de 35 m^2. Se mantienen anclados, a diferentes profundidades, dos objetos con la misma masa y volumen en cada uno de ellos como se muestra en la imagen. ¿Cuál de los objetos experimenta mayor presión? A. El objeto 1 experimenta mayor presión debido a que está en un tanque mucho más grande. B. El objeto 1 y el 3 experimentan la mayor presión, debido a que esta es independiente de la cantidad de liquido. C. El objeto 3, porque se encuentra a mayor profundidad y en un recipiente que contiene menor cantidad de agua. D. Los cuatro objetos presentan la misma presión, porque están sumergidos en agua que presenta la misma densidad.