Answer:
c is all the points in the open interval (0,25)
Step-by-step explanation:
Here given is a function
, which is continuous in the interval [0,25] and differentiable in (0,25)
Mean value theorem says there exists at least one c in the interval (0,25) such that
We have
For the given function
Hence we have c equals all the points in the open interval (0,25)
Answer:
a) P(x=3)=0.089
b) P(x≥3)=0.938
c) 1.5 arrivals
Step-by-step explanation:
Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.
The variable X is modeled by a Poisson process with a rate parameter of λ=6.
The probability of exactly k arrivals in a particular hour can be written as:
a) The probability that exactly 3 arrivals occur during a particular hour is:
b) The probability that <em>at least</em> 3 people arrive during a particular hour is:
c) In this case, t=0.25, so we recalculate the parameter as:
The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.