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28 April, 17:30

A normal distribution of values has a mean of 47 and a standard deviation of 3.2. Which of the numbered choices is the percentage of values that lie between 42 and 50?

1) 17.4% 2) 59.1% 3) 76.7% 4) 82.4%

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  1. 28 April, 17:57
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    Given:

    μ = 47, population mean

    σ = 3.2, population standard deviation

    When the random variable is x = 42, the - score is

    z = (42 - 47) / 3.2 = - 1.5625

    From normal tables, the area to the left of is

    0.0591 = 5.91%

    When x = 50,

    z = (50 - 47) / 3.2 = 0.9375

    The area to the left of z is

    0.8257 = 82.57%

    Therefore the area between x = 42 and x=50 is

    82.57 - 5.91 = 76.66%

    Answer: 3)

    The correct answer is 76.7%
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