A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. F

Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.

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Kiệt Gia 4 years 2021-08-04T01:07:17+00:00 1 Answers 31 views 0

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  1. quangkhai
    0
    2021-08-04T01:09:14+00:00
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    Answer:

    0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.

    Step-by-step explanation:

    Uniform probability distribution:

    An uniform distribution has two bounds, a and b.

    The probability of finding a value between c and d is:

    P(c \leq X \leq d) = \frac{d - c}{b - a}

    Uniformly distributed between 47.0 and 57.0 minutes.

    This means that a = 47, b = 57

    Find the probability that a given class period runs between 51.25 and 51.5 minutes.

    P(c \leq X \leq d) = \frac{51.5 - 51.25}{57 - 47} = 0.025

    0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.

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