This Exercise Is Based on the Following Information, Gathered from Student

question 58

Short Answer

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) It can be shown that if X and Y are independent normal random variables with means $\mu _ { X }$ and $\mu _ { y }$ and standard deviations $\sigma _ { X }$ and $\sigma _ { y }$ respectively, then their sum $X + Y$ is also normally distributed and has mean $\mu = \mu _ { X } + \mu _ { Y }$ and standard deviation $\sigma = \sqrt { \sigma ^ { 2 } X + \sigma ^ { 2 } Y }$ . Assuming that the time it takes a student to complete each task is independent of the others, find the probability that a student will take at least 20 minutes to complete both Tasks 3 and 4. Round your answer to four decimal places. Round Z to two decimal places. $$\begin{array} { | l | l | l | } \hline \text { Task } & \begin{array} { l } \text { Mean Time } \\( \text { minutes } )\end{array} & \begin{array} { l } \text { Standard } \\\text { Deviation }\end{array} \\\hline \text { Task 1: Descriptive Analysis of Data } & 11.4 & 5.0 \\\hline \text { Task 2: Standardizing Scores } & 11.9 & 9.0 \\\hline \text { Task 3: Poisson Probability Table } & 7.3 & 3.9 \\\hline \text { Task 4: Areas Under Normal Curve } & 9.1 & 5.5 \\\hline\end{array}$$

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Definitions:

Capital

Financial assets or the financial value of assets, such as cash and securities, owned by an individual or organization, especially those used to start or operate a business.

Market Value

The current quoted price at which an asset or service can be bought or sold in a public marketplace.

Economic Condition

Refers to the current state of the economy in a particular area or globally, often evaluated based on factors like GDP, employment rates, and inflation.

Credit Risk

The possibility that a borrower may default on any type of debt by failing to make required payments.