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27 March, 01:52

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 37 and a standard deviation of 9. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 28 and 46?

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  1. 27 March, 01:53
    0
    0.6826

    Step-by-step explanation:

    Mean (μ) = 37

    Standard deviation (σ) = 9

    P (28 < x < 46) = ?

    Using normal distribution

    Z = (x - μ) / σ

    For x = 28

    Z = (28 - 37) / 9

    Z = - 9/9

    Z = - 1

    For x = 46

    Z = (46 - 37) / 9

    Z = 9/9

    Z = 1

    We now have

    P (-1 < Z < 1)

    = P (Z < 1) - P (Z < - 1)

    From the table, Z = 1 = 0.3413

    φ (Z) = 0.3413

    Recall that

    When Z is positive, P (x
    P (Z<1) = 0.5 + 0.3413

    = 0.8413

    When Z is negative, P (x
    P (Z< - 1) = 0.5 - 0.3413

    = 0.1587

    We now have

    0.8413 - 0.1587

    = 0.6826
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