Question

In: Statistics and Probability

4. The number of students arriving at a university’s health center is Poisson distributed with a...

4. The number of students arriving at a university’s health center is Poisson distributed with a mean of 4.5 students
per hour. Use the appropriate formulas provided in class to determine the probability that:
a. four students will arrive at the health center in the next hour.
b. more than 10 minutes will elapse between student arrivals at the health center.

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Expert Solution

SOLUTION:

From given data,

4). The number of students arriving at a university’s health center is Poisson distributed with a mean of 4.5 students per hour. Use the appropriate formulas provided in class to determine the probability that:

Poisson distributed with a mean of 4.5 students per hour

a) four students will arrive at the health center in the next hour.

P(four students will arrive at the health center in the next hour)=P(X=4)

=e-4.5*4.54/4!

=0.189808

b) more than 10 minutes will elapse between student arrivals at the health center.

expected student in 10 minute =10*4.5/60=0.75

P( more than 10 minutes will elapse between student arrivals at the health center)=P(no student in 10 minutes)

=e-0.75*0.750/0!

=0.472367

orchestra answered 2 years ago
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