DEPARTMENT OF STUDIES \& RESEARCH IN MANAGEMENT KARNATAKA STATE OPEN UNIVERSITY Mukthagangotri, Mysuru - 570006
MBA 1st SEMESTER INTERNAL ASSIGNMENT
Academic Year 2023-24 January Cycle
MBHC-1.4: Statistics and Optimization Techniques (Answer any two)
\[
10 \times 2=20
\]
1. Prove that median lies between mean and mode from following data.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline Heights in cms & \( 120-125 \) & \( 125-130 \) & \( 130-135 \) & \( 135-140 \) & \( 140-145 \) & \( 145-150 \) \\
\hline No. of Children & 7 & 10 & 18 & 25 & 13 & 7 \\
\hline
\end{tabular}
2. The following data represents the marks in Algebra (x) and Geometry (y) of a group of 10 students. Find both the regression equations and hence estimate \( \mathbf{y} \) if \( \mathbf{x}=\mathbf{7 8} \) and \( \mathbf{x} \) if \( \mathbf{y}=\mathbf{9 4} \).
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline \( \mathbf{x} \) & 75 & 80 & 93 & 65 & 87 & 71 & 98 & 68 & 89 & 77 \\
\hline \( \mathbf{y} \) & 82 & 78 & 86 & 72 & 91 & 80 & 95 & 72 & 89 & 74 \\
\hline
\end{tabular}
3. Mean and Standard deviation of chest measurements of 1200 soldiers are \( 85 \mathrm{cms} \) and \( 5 \mathrm{cms} \) respectively. How many of them are expected to have chest measurements exceeding \( 95 \mathrm{cms} \), assuming the measurements follow the normal distribution. How many soldiers have their chest measurements between \( 80 \mathrm{cms} \) and \( 90 \mathrm{cms} \).
4. Find the optimum schedule for the given projects. The overhead cost is ?75 per day.
\begin{tabular}{|c|c|c|c|c|}
\hline \multirow[b]{2}{*}{ Activity } & \multirow[b]{2}{*}{ Predecessor } & \multicolumn{2}{|c|}{ Duration (days) } & \multirow{2}{*}{\begin{tabular}{c}
Increase in cost for \\
crashing by one day \\
?
\end{tabular}} \\
\hline & & \begin{tabular}{c}
Normal \\
Time
\end{tabular} & \begin{tabular}{l}
Crash \\
Time
\end{tabular} & \\
\hline \( \mathrm{A} \) & - & 3 & 2 & 150 \\
\hline B & - & 4 & 3 & 100 \\
\hline \( \mathrm{C} \) & \( \mathrm{A} \) & 5 & 4 & 200 \\
\hline \( \mathrm{D} \) & \( \mathrm{A} \) & 7 & 5 & 300 \\
\hline \( \mathrm{E} \) & \( \mathrm{B}, \mathrm{C} \) & 3 & 3 & 0 \\
\hline \( \mathrm{F} \) & \( \mathrm{B}, \mathrm{C}, \mathrm{D} \) & 6 & 2 & 75 \\
\hline
\end{tabular}
a) Draw the Project using normal duration.
b) Find the path and projects duration for above.
c) Find the optimal schedule and project duration.
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