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Katie must take five exams in a math class. If her scores on the first four exams are 77, 79, 95, and 93, what score must Katie get on the fifth exam for her overall mean to be at least 80?
The maximum score on an exam is 100 points. If it is not possible for Katie to achieve the required score on the exam, type np in the answer blank.

Katie needs to get a

  • stats -

    x1 = 77

    x2 = 79

    x3 = 95

    x4 = 93


    averagge of five exam:

    ( x1 + x2 + x3 + x4 + x5 ) / 5 = 80

    ( 77 + 79 + 95 + 93 + x5 ) / 5 = 80

    ( 344 + x5 ) / 5 = 80 Multiply both sides by 5

    344 + x5 = 80 * 5

    344 + x5 = 400 Subtract 344 to both sides

    x5 = 400 - 344 = 56


    Answer:

    Greater or equal 56


    Proof :

    ( x1 + x2 + x3 + x4 + x5 ) / 5 =

    ( 77 + 79 + 95 + 93 + 56 ) / 5 =

    400 / 5 = 80

  • stats -

    Katie must get 56 or more because ...

    1) 77 77
    2) 79 79
    3) 95 95
    4) 93 + 93
    -------
    344+56= 400
    Divide 400 by 5 which equals 80

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