Respuesta :
Answer:
b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941
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 uniform probability distribution is:
[tex]M = \frac{a + b}{2}[/tex]
The standard deviation of the uniform 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]
Uniform distribution between 2.93 and 3.1 volts
This means that [tex]a = 2.93, b = 3.1[/tex]. So
Mean:
[tex]M = \frac{2.93 + 3.1}{2} = 3.015[/tex]
Standard deviation:
[tex]S = \sqrt{\frac{(3.1 - 2.93)^{2}}{12}} = 0.049[/tex]
What is the probability that a battery has a voltage less than 2.98?
[tex]P(X \leq 2.98) = \frac{2.98 - 2.93}{3.1 - 2.93} = 0.2941[/tex]
So the correct answer is:
b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941
