1.It has been found that IQ scores are normally distributed

1个回答

  • You probably need a table on normal distribution to do this.

    a.

    (80 -108)/16 = -28/16 = -1.75σ

    The area between 0 and -1.75σ is 0.4599

    the proportion of persons with an IQ score of 80 points or less is 0.5 - 4599 = 0.0401

    b.

    (100 - 108)/16 = -0.5σ,the area between 0 and -0.5σ is 0.1915

    (120 - 108)/16 = 0.75σ,the area between 0 and 0.75σ is 0.2734

    They (100 and 120) are on opposite side of the average,the probability that a person randomly chosen will have an IQ score between 100 and 120 points is 0.1915 + 0.2734 = 0.4649

    c.

    the percentage of people below the average is 50%,so we need to find out which σ corresponds to 0.48 on the right side of the average.From the table,the value is between 2.55σ and 2.56σ

    2.55σ:2.55*16 + 108 = 148.8

    2.56σ:2.56*16 + 108 = 148.96

    the minimum score is 149

    d.

    Between 25% and average,the probability is 0.5 - 0.25 = 0.25

    0.25 corresponds to a value between 0.67σ and 0.68σ

    0.67σ:108 - 0.67*16 = 97.28

    0.68σ:108 - 0.68*16 = 97.12

    the maximum score is 97