The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uni

Question

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 31 and 55 minutes. One student is selected at random.
1. Find the probability of the following events.
A. The student requires more than 51 minutes to complete the quiz.
B. The student completes the quiz in a time between 35 and 42 minutes.
C. The student completes the quiz in exactly 41.84 minutes.

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Amelia 2 weeks 2021-09-13T15:22:46+00:00 1 Answer 0

Answers ( )

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    2021-09-13T15:24:05+00:00

    Answer:

    A. p = 0.1667

    B. p = 0.29167

    C. p = 0.04167

    Step-by-step explanation:

    If the time for complete a quiz follows a uniform distribution, the probability that a student finish the quiz in x minutes is:

    p(x) = 1/(b-a)    for x between a and b

    Where, a and b are the limits of the distribution. So, replacing b by 55 minutes and a by 31 minutes, we get:

    p(x) = 1/(55-31) = 0.04167

    It means that the probability that a student completes the quiz in exactly 41.84 minutes is 0.04167

    Additionally, the probability that a student finish in x minutes of less is calculated as:

    p(X<x) = (x-a)/(b-a)  for x between a and b

    So, replacing values, we get:

    p(X<x) = (x-31)/(55-31) = (x-31)/24

    Then, the probability that a student requires more than 51 minutes to complete the quiz is calculated as:

    p(x>51)=1-p(x<51)=1-\frac{51-31}{24}=1-\frac{5}{6}=0.1667

    Finally, the probability that a  student completes the quiz in a time between 35 and 42 minutes is calculated as:

    p(35<x<42)=p(x<42)-p(x<35)=\frac{42-31}{55-31}-\frac{35-31}{55-31}=0.4583-0.1667

    p(35<x<42)=0.2916

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45:7+7-4:2-5:5*4+35:2 =? ( )