Respuesta :
Answer:
(A) 0.15625
(B) 0.1875
(C) Can't be computed
Step-by-step explanation:
We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.
Let X = Amount of time taken by student to complete a statistics quiz
So, X ~ U(32 , 64)
The PDF of uniform distribution is given by;
f(X) = [tex]\frac{1}{b-a}[/tex] , a < X < b where a = 32 and b = 64
The CDF of Uniform distribution is P(X <= x) = [tex]\frac{x-a}{b-a}[/tex]
(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)
P(X > 59) = 1 - P(X <= 59) = 1 - [tex]\frac{x-a}{b-a}[/tex] = 1 - [tex]\frac{59-32}{64-32}[/tex] = [tex]1-\frac{27}{32}[/tex] = 0.15625
(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)
P(X <= 43) = [tex]\frac{43-32}{64-32}[/tex] = [tex]\frac{11}{32}[/tex] = 0.34375
P(X < 37) = [tex]\frac{37-32}{64-32}[/tex] = [tex]\frac{5}{32}[/tex] = 0.15625
P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875
(C) Probability that student complete the quiz in exactly 44.74 minutes
= P(X = 44.74)
The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.
