Use the following data to answer the questions posed below.  This is data taken from a simple random sample of students in a class from a large  population.  The variables are defined as follows: Student: Student ID. Credits: # of credits earned GPA: Current College GPA Student’s Gender: Male/Female Program:  Program of study Final Exam: Students’ scores on final exam SATM: Students’ SAT math scores The data are as follows student    credits      gpa        gender     program Final Exam   SATM      1 42 3.00 female Business 42.5 410 2 42 3.49 male Business 77.5 440 3 45 3.72 female Business 75.0 390 4 45 3.39 male Business 70.0 550 5 100 3.39 male Arts & Sciences    92.5 560 6 43 3.36 male Arts & Sciences 72.5 600 7 69 2.83 female Business 75.0 460 8 28 2.86 male Arts & Sciences 77.5 520 9 25 3.68 male Arts & Sciences 82.5 600 10 42 1.68 female Business 52.5 540 11 45 2.89 female Business 65.0 440 12 42 3.15 male Business 45.0 550 13 69 3.18 female Business 57.5 480 14 45 3.11 male Business 42.5 590 15 37 2.32 female Arts & Sciences 47.5 440 16 45 2.86 male Business 62.5 590   Based on the cross tabulation, here is the joint probability table between events M and B, where M is the event that the individual is male, and B is the event that the individual is a business major.          B           B^C                               M         0.31 0.06 0.44        M^C 0.38 0.25 0.56   0.69 0.31 1.00   Based on this information, please compute each of the following, rounding your answers to two decimal points.  = P(M\B^C) =  = P(B^C\M) =  = P (M ∩ B^C) =

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  1. Use the following data to answer the questions posed below.  This is data taken from a simple random sample of students in a class from a large  population.  The variables are defined as follows:

    • Student: Student ID.
    • Credits: # of credits earned
    • GPA: Current College GPA
    • Student’s Gender: Male/Female
    • Program:  Program of study
    • Final Exam: Students’ scores on final exam
    • SATM: Students’ SAT math scores

    The data are as follows

    student    credits      gpa        gender     program Final Exam   SATM     
    1 42 3.00 female Business 42.5 410
    2 42 3.49 male Business 77.5 440
    3 45 3.72 female Business 75.0 390
    4 45 3.39 male Business 70.0 550
    5 100 3.39 male Arts & Sciences    92.5 560
    6 43 3.36 male Arts & Sciences 72.5 600
    7 69 2.83 female Business 75.0 460
    8 28 2.86 male Arts & Sciences 77.5 520
    9 25 3.68 male Arts & Sciences 82.5 600
    10 42 1.68 female Business 52.5 540
    11 45 2.89 female Business 65.0 440
    12 42 3.15 male Business 45.0 550
    13 69 3.18 female Business 57.5 480
    14 45 3.11 male Business 42.5 590
    15 37 2.32 female Arts & Sciences 47.5 440
    16 45 2.86 male Business 62.5 590

     

    Based on the cross tabulation, here is the joint probability table between events M and B, where M is the event that the individual is male, and B is the event that the individual is a business major.

             B           B^C                       
           M         0.31 0.06 0.44
           M^C 0.38 0.25 0.56
      0.69 0.31 1.00

     

    Based on this information, please compute each of the following, rounding your answers to two decimal points.

    1.  = P(M\B^C) =
    2.  = P(B^C\M) =
    3.  = P (M ∩ B^C) =
    4.  = P(B) = 
    5.  = P(B^C ∪ M^C) =
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