Question

Assume that voltages in a circuit vary between 6 volts and 12 volts, and voltages are spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of voltage levels. In each case, draw a sketch and leave answers as a fraction. a. Greater than 10 volts b. Less than 11 volts c. Between 6.5 volts and 8 volts

Answer 1

Answer:

a) $P(X>10) =1-P(X$

b) $P(X$

c) $P(6.5$

In the figure attached we have the illustration for the probability for each part.

Step-by-step explanation:

For this case we define the random variable X as the voltages in a circuit  and the distribution for X is given by:

$X \sim Unif (a= 6, b=12)$

Part a

we want this probability:

$P(X>10)$

We can use the cumulative distirbution function given by:

$F(x) = \frac{x-a}{b-a}, a\leq X \leq b$

And using the complement rule we have this:

$P(X>10) =1-P(X$

Part b

We want this probability:

$P(X$

And using the cumulative distirbution function we got:

$P(X$

Part c

We want this probability:

$P(6.5$

And using the cumulative distirbution function we got:

$P(6.5$

In the figure attached we have the illustration for the probability for each part.