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15 March, 10:37

A normal distribution has a mean of 142 and a standard deviation of 16.

What is the probability that a randomly selected value lies between 142 and 174?

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Answers (2)
  1. 15 March, 10:44
    0
    Let x be a random variable in the population.

    P (142 < x < 174) = P ((142 - 142) / 16 < z < (174 - 142) / 16) = P (0 < z < 2) = P (z < 2) - P (z < 0) = 0.97725 - 0.5 = 0.47725
  2. 15 March, 10:55
    0
    Mean = 142;

    Standard Deviation ("Sigma") = 16

    172 = 142 + 32 = 142 + 2 * 16 = Mean + 2 Standard Deviation

    It means that between 142 and 174 lies:

    34 % + 13.5 % = 47.5 % of all values.

    The probability that a randomly selected value lies between 142 and 174 is:

    P = 0.475
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