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

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. $$\begin{array} { | l | l | l | } \hline \text { Task } & \begin{array} { l } \text { Mean Time } \\( \text { minutes } )\end{array} & \begin{array} { l } \text { Standard } \\\text { Deviation }\end{array} \\\hline \text { Task 1: Descriptive Analysis of Data } & 11.4 & 5.0 \\\hline \text { Task 2: Standardizing Scores } & 11.9 & 9.0 \\\hline \text { Task 3: Poisson Probability Table } & 7.3 & 3.9 \\\hline \text { Task 4: Areas Under Normal Curve } & 9.1 & 5.5 \\\hline\end{array}$$