Statistics Undergrad Course

Question

Determine the area under the standard normal curve that lies…….

A) To the left of -2.34 or to the right of 645.

B) Between -0.88 and 55

C) To the left of -1 or to the right of 2

D) Between 1.48 and 2.82

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Data Interpretation Delphene Marie 5 months 3 Answers 131 views 0

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Answers ( 3 )

  1. Hi there! Thanks for asking this question.

    To start with the standard normal curve, the values are found out with a table called Biometrika. However, various universities/books/authors/courses use different tables. Just wanted to know which table you are using.

    I am using this table:

    Basic Concept: Middle value is 0 and areas on each side are 0.5, so total area 1 under the complete curve.

    Example calculations:

    1. The area to the left of 1:
      From the table, the area from 0 to 1 is 0.3413.
      And, the area to the left of 0 is 0.5.
      So, total area to the left of 1 is 0.5 + 0.3413 = 0.8413
    2. The area to the left of -1:
      Negative values need assistance from their positive counterparts.
      -1 has its counterpart 1.
      To the left of -1, lies the same area which lies to the right of 1.
      From the table, the area between 0 and 1 = 0.3413
      So, the area beyond 1 = 0.5 – 0.3413 = 0.1587
      So, this will be the required area to the left 0f -1.

    Now let’s come to the first two parts of your question. 645 and 55 are values which are too high for standard normal distribution. They almost touch the line and the area beyond those doesn’t matter. This is so because 99.27% area under the normal curve lies between -3 and 3.

     

    Your answers are here:

    A. To the left of -2.34:
    Means, to the right of 2.34.
    From the table, the area between 0 and 2.34 = 0.4904
    So, the area to the right of 2.34 = 0.5 – 0.4904 = 0.0096
    So, required area is 0.0096

    To the right of 645: Almost zero area.

    B. Between -0.88 and 55:
    Means to the right of -0.88, because the area to the right of 55 would be negligible, so counting it or not doesn’t matter.
    The area to the right of -0.88 = the area to the left of 0.88
    = 0.5 + the area between 0 and 0.88
    = 0.5 + 0.3106
    = 0.8106

    C. To the left of -1: (described in the example above) = 0.1587
    To the right of 2: From the table, the area between 0 and 2 = 0.4772
    So, the area to the right of 2 = 0.5 – 0.4772 = 0.0228

    D. Between 1.48 and 2.82:
    (i) The area between 0 and 1.48 (From table) = 0.4306
    (ii) The area between 0 and 2.82 (From table) = 0.4976
    So, the area between 1.48 and 2.82 = 0.4976 – 0.4306 = 0.0670

    Best answer

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