A random variable X is uniformly distributed over the interval (48, 96).
Find the following probabilities.
a) P(50 < X < 70)
b) P(X < 75)
c) P(X > 90)
d) P(X < 60 or X > 80)

a)

b)

c)

d)

And using the CDF we got:

And using the CDF and the complement rule we got:

So then the probability required would be:

P(X < 60 or X > 80) = 0.25+0.333= 0.583

Step-by-step explanation:

For this case we define the random variable of interest X, and we know the distribution given by:

The density function is given by:

And the cumulative distribution function is given by:

Part a

We want this probability:

And we can find this probability with this difference:

And replacing we got:

Part b

We want this probability:

And using the CDF we got:

Part c

We want this probability:

And using the CDF and the complement rule we got:

Part d

And using the CDF we got:

And using the CDF and the complement rule we got:

So then the probability required would be:

P(X < 60 or X > 80) = 0.25+0.333= 0.583

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

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step-by-step explanation:

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