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15 April, 09:55

Suppose a normal distribution has a mean of 48 and a standard deviation of 2. What is the probability that a data value is between 43 and 46? Round your answer to the nearest tenth of a percent.

A. 17.2%

B. 16.3%

C. 14.2%

D. 15.2%

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  1. 15 April, 11:26
    0
    Choice D. 15.2%

    Step-by-step explanation:

    We have a normal ...

    mean u = 48

    standard deviation s = 2

    We want P (43 < X < 46)

    We standardize.

    Consider P (43 < X) = P ((43 - 48) / 2 < Z) = P (-2.5 < Z)

    P (X < 46) = P (Z < (46 - 48) / 2) = P (Z < - 1)

    We want P (-2.5 < Z < - 1)

    Look at Z-scores.

    P (Z < - 2.5) = 0.0062

    P (Z < - 1) = 0.1587

    so P (-2.5 < Z < - 1) = P (Z < - 1) - P (Z < - 2.5) = 0.1587 - 0.0062 = 0.1525 = 15.2%

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