Respuesta :
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:
[tex]p(x>51)=1-p(x<51)=1-\frac{51-31}{24}=1-\frac{5}{6}=0.1667[/tex]
Finally, the probability that a student completes the quiz in a time between 35 and 42 minutes is calculated as:
[tex]p(35<x<42)=p(x<42)-p(x<35)=\frac{42-31}{55-31}-\frac{35-31}{55-31}=0.4583-0.1667[/tex]
[tex]p(35<x<42)=0.2916[/tex]
