Questions: Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give questionnaires to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 14. The lowest possible score from those who are not "risk averse" is 10, are described as "risk neutral." What is the questionnaire score that separates the bottom 10% are classified as "risk averse" from those who are not? Can you answer to the decimal place: Round your answer to one decimal place. X > Statistical Literacy and Critical Reasoning 8:34 AM Sun, Oct 20 Normal Distribution: Finding a Raw Score

Solution Steps

To find the questionnaire score that separates the bottom 10% from the rest, we need to determine the z-score that corresponds to the 10th percentile of a standard normal distribution. Then, we use the mean and standard deviation of the questionnaire scores to convert this z-score into the actual score. Since the standard deviation is not provided, we will assume a standard deviation of 1 for this calculation.

To find the score that separates the bottom 10% of the distribution, we first need to find the z-score corresponding to the 10th percentile. Using the standard normal distribution, we find:

\[ z = -1.2816 \]

Next, we use the z-score to calculate the actual score using the formula:

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

where:

• \( \mu = 14 \) (mean score)
• \( z = -1.2816 \) (z-score for the 10th percentile)
• \( \sigma = 1 \) (assumed standard deviation)

Substituting the values, we have:

\[ X = 14 + (-1.2816) \cdot 1 = 14 - 1.2816 = 12.7184 \]

Finally, we round the calculated score to one decimal place:

\[ X \approx 12.7 \]

Final Answer