Respuesta :
Answer:
a) The mean connection speed is 1 MBPS and the standard deviation is 0.1443 MBPS.
b) 10% probability that the connection speed will be less than 0.8 MBPS at any given time
c) 50% probability that the connection speed will be between 0.875 MBPS and 1.125 MBPS at any given time
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 mean of the distribution is:
[tex]M = \frac{a + b}{2}[/tex]
The standard deviation of the distribution is:
[tex]S = \sqrt{\frac{(b-a)^{2}{12}}[/tex]
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
The probability that we find a value of x between two values, c and d, d greater than c, is given by
[tex]P(c \leq x \leq d) = \frac{d - c}{b - a}[/tex]
Assuming X is uniformly distributed on the interval 0.75 to 1.25 MBPS, answer the following questions
This means that [tex]a = 0.75, b = 1.25[/tex]
a) Find the mean connection speed and standard deviation.
[tex]M = \frac{a + b}{2} = \frac{0.75 + 1.25}{2} = 1[/tex]
[tex]S = \sqrt{\frac{(b-a)^{2}{12}} = \sqrt{\frac{(1.25 - 0.75)^{2}{12}} = 0.1443[/tex]
The mean connection speed is 1 MBPS and the standard deviation is 0.1443 MBPS.
b) What is the probability that the connection speed will be less than 0.8 MBPS at any given time?
[tex]P(X \leq 0.8) = \frac{0.8 - 0.75}{1.25 - 0.75} = 0.1[/tex]
10% probability that the connection speed will be less than 0.8 MBPS at any given time
c) What is the probability that the connection speed will be between 0.875 MBPS and 1.125 MBPS at any given time?
[tex]P(0.875 \leq x \leq 1.125) = \frac{1.125 - 0.875}{1.25 - 0.75} = 0.5[/tex]
50% probability that the connection speed will be between 0.875 MBPS and 1.125 MBPS at any given time
