Math Problem Statement
The mean of 1,000 quarterly returns is calculated as 4.52%. The standard deviation of these returns is calculated as 1.84%. An investor can be 95% certain that the return for any particular quarter will be at least: Group of answer choices
0.84%
4.29%
1.37%
2.68%
4.52%
Solution
To solve this problem, we can use the concept of a confidence interval for a normal distribution.
Given:
- Mean () = 4.52%
- Standard deviation () = 1.84%
- Confidence level = 95%
A 95% confidence interval corresponds to 1.96 standard deviations below and above the mean.
The lower bound of the interval can be calculated as:
Substituting the values:
Rounding to two decimal places, the closest answer is 0.84%.
Therefore, the correct answer is 0.84%.
Would you like more details on how this was calculated or have any other questions?
Here are some related questions you might find interesting:
- How is the 1.96 value for the 95% confidence interval derived?
- What would the confidence interval be if the confidence level was 90% instead?
- How do we interpret the standard deviation in the context of this problem?
- What is the significance of the mean return in this scenario?
- How would the interval change if the standard deviation was higher?
Tip: The 1.96 factor is used for 95% confidence intervals because it corresponds to the z-value that cuts off the central 95% of a standard normal distribution.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Normal Distribution
Confidence Intervals
Formulas
Confidence interval for a normal distribution
Theorems
-
Suitable Grade Level
Undergraduate level
Related Recommendation
95% Confidence Interval for Asset Returns with Mean 10.55% and Standard Deviation 20.46%
Calculating Expected Range of Returns with 68 Percent Probability in a Normal Distribution
Calculate 90% Confidence Interval for Mean Daily Stock Return
Calculate 90% Confidence Interval for Mean Daily Stock Return
95% Confidence Interval for Stock Returns Over 5 Years