so important, can anyone solve it please! The number of calls (X)that arrive at
ID: 3200190 • Letter: S
Question
so important, can anyone solve it please!The number of calls (X)that arrive at a hotel reception is modeled as a Poisson distribution with an average of 6 calls per hour. calls/min 1-What is the probability that there are exactly 5 calls in one hour? hat is the probability that there are exactly 4 calls in 2 hours? Now, we are interested in the time between calls. Let t(in minutes) be the random variable representing the time between calls. 3- What is the distribution (type and parameters) oft and what is the mean time between calls (expected value of t T 4-What is the probability that the first call arrives to the reception within 20 min of interval? 5-Use the conditional probability ruleto calculate the probability that the reception receive a call in the next 30 min, giving that the reception has not had a call in the first 10 min?. Compare and comment on the results to question (4). T
Explanation / Answer
Answer to question# 1)
The number of calls follows a poisson distribution
The mean Lambda ()= 6 calls per hour
.
We need to find the probability of getting exactly 5 calls in one hour
thus we need to find the probability P(x=5)
The formula of Poisson distribution is:
P(x=5) = e^- * ^x / x!
We have = 6
x = 5
on plugging these values we get:
P(X=5) = e^-6 * (6)^5/ 5!
P(X=5) = 0.1606
.
Thus the answer for question# 1 is P(X=5) = 0.1606
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