Respuesta :
Answer:
a) The expected arrival time is 2.25 minutes.
b) 25.88% probability that an elevator arrives in less than 1.1 minutes
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X < x) = \frac{x - a}{b-a}[/tex]
The expected value of the uniform distribution is given by:
[tex]M = \frac{a+b}{2}[/tex]
The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4.5 minutes.
This means that [tex]a = 0, b = 4.5[/tex]
a. Calculate the expected arrival time. (Round your answer to 2 decimal place.)
[tex]M = \frac{a+b}{2} = \frac{0 + 4.5}{2} = 2.25[/tex]
The expected arrival time is 2.25 minutes.
b. What is the probability that an elevator arrives in less than 1.1 minutes
[tex]P(X < 1.1) = \frac{1.1 - 0}{4.25 - 0} = 0.2588[/tex]
25.88% probability that an elevator arrives in less than 1.1 minutes
