What is the volume enclosed by the slanted prism in the diagram?
2 answers:
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A parallelogram by definition is a four-sided figure with opposite sides that are parallel.
If that's the case, the length of opposite sides should be the same as well, meaning that:
then,
find AB
A
Answer:
a) The expected number of calls in one hour is 30.
b) There is a 21.38% probability of three calls in five minutes.
c) There is an 8.2% probability of no calls in a five minute period.
Step-by-step explanation:
In problems that we only have the mean during a time period can be solved by the Poisson probability distribution.
Poisson probability distribution
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
is the mean in the given interval.
a. What is the expected number of calls in one hour?
Calls come in at the rate of one each two minutes. There are 60 minutes in one hour. This means that the expected number of calls in one hour is 30.
b. What is the probability of three calls in five minutes?
Calls come in at the rate of one each two minutes. So in five minutes, 2.5 calls are expected, which means that . We want to find P(X = 3).
There is a 21.38% probability of three calls in five minutes.
c. What is the probability of no calls in a five-minute period?
This is P(X = 0) with .
There is an 8.2% probability of no calls in a five minute period.
Let be the constant factor between terms, so that
and so on, with
(notice how the exponent and the subscript add to )
Then
so if
then
Now,
so the third term in the sequence is 30.