Respuesta :
Answer:
a) 0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.
b) 0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.
c) 0% probability that the student completes the quiz in exactly 37.23 minutes.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniformly distributed between 30 and 60 minutes.
This means that [tex]a = 30, b = 60[/tex]
a. The student requires more than 55 minutes to complete the quiz.
[tex]P(X > 55) = \frac{60 - 55}{60 - 30} = 0.1667[/tex]
0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.
b. The student completes the quiz in a time between 30 and 40 minutes.
[tex]P(30 \leq X \leq 40) = \frac{40 - 30}{60 - 30} = 0.3333[/tex]
0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.
c. The student completes the quiz in exactly 37.23 minutes.
Probability of an exact value in a continuous distribution, such as the uniform distribution, is 0%, so:
0% probability that the student completes the quiz in exactly 37.23 minutes.
