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7 June, 21:42

IQ scores for adults age 20 to 34 years are normally distributed according to N (120, 20). About what percent of people in this group scored above 140?

68%

34%

16%

13.5%

2.5%

+3
Answers (1)
  1. 7 June, 23:46
    0
    Answer: 16%

    Step-by-step explanation:

    Since the IQ scores for adults age 20 to 34 years are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = IQ scores for adults age 20 to 34 years.

    µ = mean score

    σ = standard deviation

    From the information given,

    µ = 120

    σ = 20

    We want to find the probability of people in this group scored above 140. It is expressed as

    P (x > 140) = 1 - P (x ≤ 140)

    For x = 140,

    z = (140 - 120) / 20 = 1

    Looking at the normal distribution table, the probability corresponding to the z score is 0.84134

    P (x > 140) = 1 - 0.84134 = 0.15866

    Approximately 0.16

    Therefore, the percent of people in this group scored above 140 is

    0.16 * 100 = 16%
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