Exam 1

  1. Question

    Given the following information:

    banana ++ pineapple ++ banana = 417417
    orange ++ banana ++ orange = 266266
    banana ++ pineapple ++ pineapple = 600600

    Compute:

    banana ++ orange ++ pineapple = ?\text{?}

    1. 433433
    2. 565565
    3. 600600
    4. 261261
    5. 542542

  2. Question

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


    1. 1.1391.139
    2. 0.6710.671
    3. 1.7321.732
    4. 2.2362.236
    5. 0.2370.237

  3. Question

    What is the derivative of f(x)=x5e3.2xf(x) = x^{5} e^{3.2 x}, evaluated at x=0.8x = 0.8?


  4. Question

    The daily expenses of summer tourists in Vienna are analyzed. A survey with 121121 tourists is conducted. This shows that the tourists spend on average 136.4136.4 EUR. The sample variance sn12s^2_{n-1} is equal to 148148.

    Determine a 95%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 XX and the amount of expenses for continuing education YY (in EUR) were recorded. The statistical summary of the data set is given by:

    Variable XX Variable YY
    Mean 52 240
    Variance 149 3259

    The correlation between XX and YY 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.