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10 July, 03:39

The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If the variable is normally distributed, what is the probability that a randomly selected town will have a homicide rate greater than 14?

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  1. 10 July, 05:21
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    Answer:t

    Pr (x>14) = 0.0228

    Step-by-step explanation:

    Mean (u) = 10

    Standard deviation (α) = 2

    Number of population (n) = 100,000

    Let X be a random variable which is a measure of the town to have homicide

    For normal distribution,

    Z = (X - u) / α

    For Pr (x=14) we have

    (14 - 10) / 2

    = 4/2

    = 2

    From the normal distribution table, 2 = 0.4772

    Φ (z) = 0.4772

    Recall that:

    If Z is positive,

    Pr (x>a) = 0.5 - Φ (z)

    Pr (x>14) = 0.5 - 0.4772

    = 0.0228
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