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 49.5 and a standard devlation 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 are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

Step 1 ：The problem is asking for the score that separates the bottom 5% of customers from the rest. This is a problem of finding a percentile in a normal distribution.

Step 2 ：The z-score for the 5th percentile in a standard normal distribution is approximately -1.645. We can use this z-score, the given mean and standard deviation to find the corresponding score in the questionnaire distribution.

Step 3 ：Given that the mean is 49.5 and the standard deviation is 16, we can use the formula for converting a z-score to a raw score in a distribution: \(X = \mu + Z \sigma\), where \(X\) is the raw score, \(\mu\) is the mean, \(Z\) is the z-score, and \(\sigma\) is the standard deviation.

Step 4 ：Substituting the given values into the formula, we get \(X = 49.5 + (-1.645)(16)\).

Step 5 ：Calculating the above expression, we find that \(X \approx 23.18\).

Step 6 ：Rounding to one decimal place, we get \(X \approx 23.2\).

Step 7 ：Final Answer: The questionnaire score that separates customers who are considered risk averse from those who are not is approximately \(\boxed{23.2}\).