The age in United States has a normal distribution with a mean 46 years and standard deviation 13 years. The children are classified as thos

Question

The age in United States has a normal distribution with a mean 46 years and standard deviation 13 years. The children are classified as those younger than 18 years and the middle age citizens are those in the age group 18-55. If a citizen is randomly chosen, what is the probability that he/she is middle age

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Thành Công 1 month 2021-08-14T06:59:24+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-08-14T07:00:25+00:00

    Answer:

    0.74

    Step-by-step explanation:

    The middle age citizens are those in the age group of 18-55.

    We solve this question using z score formula

    z = (x-μ)/σ, where

    x is the raw score

    μ is the population mean

    σ is the population standard deviation.

    Mean 46 years

    Standard deviation 13 years

    For x = 18 years

    z = 18 – 46/13

    z = -2.15385

    Probability value from Z-Table:

    P(x = 18) = 0.015626

    For x = 55 years

    z = 55 – 46/13

    = 0.69231

    Probability value from Z-Table:

    P(x = 55) = 0.75563

    The probability that he/she is middle age is

    P(x = 55) – P( x = 18)

    = 0.75563 – 0.015626

    = 0.740004

    Approximately = 0.74

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