Exam 1

1. Question

   Given the following information:

   	$+$		$+$		=	$417$
   	$+$		$+$		=	$266$
   	$+$		$+$		=	$600$

   Compute:

   $+$

   $+$

   =

   $\text{?}$

   
   
   1. $433$
   2. $565$
   3. $600$
   4. $261$
   5. $542$
   
   

2. Question

   What is the distance between the two points $p = (3, 2)$ and $q = (4, 4)$ in a Cartesian coordinate system?

   
   
   1. $1.139$
   2. $0.671$
   3. $1.732$
   4. $2.236$
   5. $0.237$
   
   

3. Question

   What is the derivative of $f(x) = x^{5} e^{3.2 x}$, evaluated at $x = 0.8$?

   
   

4. Question

   The daily expenses of summer tourists in Vienna are analyzed. A survey with $121$ tourists is conducted. This shows that the tourists spend on average $136.4$ EUR. The sample variance $s^2_{n-1}$ is equal to $148$.

   Determine a $95\%$ confidence interval for the average daily expenses (in EUR) of a tourist.

   
   
   1. What is the lower confidence bound?
   2. What is the upper confidence bound?
   
   

5. Question

   For 58 firms the number of employees $X$ and the amount of expenses for continuing education $Y$ (in EUR) were recorded. The statistical summary of the data set is given by:

   	Variable $X$	Variable $Y$
   Mean	52	240
   Variance	149	3259

   The correlation between $X$ and $Y$ is equal to 0.75.

   Estimate the expected amount of money spent for continuing education by a firm with 53 employees using least squares regression.