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15.04.2020 •
Mathematics
The number of requests for assistance received by a towing service is a Poisson process with rate θ = 4 per hour.a. Compute the probability that exactly ten requests are received during a particular 2-hour period.b. If the operators of the towing service take a 30-min break for lunch, what is the probability that they do not miss any calls for assistance?c. How many calls would you expect during their break?
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Ответ:
a) 9.93% probability that exactly ten requests are received during a particular 2-hour period
b) 13.53% probability that they do not miss any calls for assistance
c) 2
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
Poisson process with rate θ = 4 per hour.
This means that
, in which n is the number of hours.
a. Compute the probability that exactly ten requests are received during a particular 2-hour period.
n = 2, so![\mu = 4*2 = 8](/tpl/images/0601/9104/b737e.png)
This is P(X = 10). So
9.93% probability that exactly ten requests are received during a particular 2-hour period
b. If the operators of the towing service take a 30-min break for lunch, what is the probability that they do not miss any calls for assistance?
n = 0.5, so![\mu = 4*0.5 = 2](/tpl/images/0601/9104/628bd.png)
This is P(X = 0). So
13.53% probability that they do not miss any calls for assistance
c. How many calls would you expect during their break?
n = 0.5, so![\mu = 4*0.5 = 2](/tpl/images/0601/9104/628bd.png)
Ответ:
It's B
The perimeter of Rectangle BCDA is 30.
The perimeter of the smaller rectangle is 22.
30/22 simplifies to 15/11
Hope this helps!