Answer:
a)
b)
c) We want to find a value c who satisfy this condition:
And using the cumulative distribution function we have this:
And solving for c we got:
Step-by-step explanation:
For this case we define the random variable X as he amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train, and we know that the distribution for X is given by:
Part a
We want this probability:
And for this case we can use the cumulative distribution function given by:
And using the cumulative distribution function we got:
For the probability if we use the cumulative distribution function and the complement rule we got:
Part b
We want this probability:
And using the cdf we got:
Part c
We want to find a value c who satisfy this condition:
And using the cumulative distribution function we have this:
And solving for c we got: