Hector is competing in a 42 mile bicycle race. He has already completed 18 miles of the race and is traveling at a constant spee
d of 12 miles per hour when Wanda starts the race. Wanda is traveling at a constant speed of 16 miles per hour. Write and solve an equation to find when Wanda will catch up to Hector. Will Wanda catch up to Hector before the race is complete? Explain. At what constant speed would Wanda travel to catch up with Hector at the finish line? Explain.
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Answer:
The probability that a randomly selected call time will be less than 30 seconds is 0.7443.
Step-by-step explanation:
We are given that the caller times at a customer service center has an exponential distribution with an average of 22 seconds.
Let X = caller times at a customer service center
The probability distribution (pdf) of the exponential distribution is given by;
Here, = exponential parameter
Now, the mean of the exponential distribution is given by;
Mean =
So, ⇒
SO, X ~ Exp()
To find the given probability we will use cumulative distribution function (cdf) of the exponential distribution, i.e;
; x > 0
Now, the probability that a randomly selected call time will be less than 30 seconds is given by = P(X < 30 seconds)
P(X < 30) =
= 1 - 0.2557
= 0.7443