Question

Your investment advisor (rich m. oney) proposes a monthly income investment scheme which promises a variable income each month. you will invest in it only if you are assured an average monthly income of more than 650 dollars. your advisor also tells you that, for the past 27 months, the scheme had incomes with an average value of 684 dollars and a standard deviation of 108 dollars. assume the income approximately follows a normal distribution.

Create a 90% two-sided confidence interval for the average monthly income of this scheme.

Answer 1

Main Answer:

The 90% two-sided confidence interval for the average monthly income of the investment scheme is $652.67 to $715.33.

Step-by-step explanation:

In statistical terms, a confidence interval provides a range of values within which we can reasonably expect the true parameter—in this case, the average monthly income—to fall. The given information about the scheme's past performance allows us to calculate a confidence interval based on the sample mean and standard deviation. The average monthly income of $684 serves as the point estimate, while the standard deviation of $108 accounts for the variability in monthly incomes.

A 90% two-sided confidence interval means we want to capture the true average income with 90% confidence. Utilizing the normal distribution assumption, we calculate the margin of error by considering the standard deviation and the critical value associated with a 90% confidence level. The resulting range of $652.67 to $715.33 signifies our confidence that the true average monthly income of the scheme lies within this interval.

Investors seeking assurance of an average monthly income exceeding $650 can be reasonably confident in the scheme's historical performance. The narrower confidence interval indicates a higher level of precision in our estimate, giving investors a more defined range for their expectations.

Answer 2

To create a 90% two-sided confidence interval for the average monthly income of the investment scheme, we can use the formula CI = average income ± (Z * (standard deviation / √n)), where CI is the confidence interval, Z is the Z-score corresponding to the desired confidence level, standard deviation is the standard deviation of the incomes, and n is the sample size (number of months). In this case, the confidence interval is approximately $652.45 to $715.55.

Step-by-step explanation:

To create a confidence interval for the average monthly income of the investment scheme, we can use the formula:

CI = average income ± (Z * (standard deviation / √n))

Where CI is the confidence interval, Z is the Z-score corresponding to the desired confidence level, standard deviation is the standard deviation of the incomes, and n is the sample size (number of months).

In this case, since it is a two-sided confidence interval and we want a 90% confidence level, the Z-score will be approximately 1.645.

Plugging in the values, we get:

CI = 684 ± (1.645 * (108 / √27))

Simplifying, the confidence interval for the average monthly income of the scheme is approximately $652.45 to $715.55.