Answer:
Step-by-step explanation:
We are given the following in the question:
Let P be the number of professor and S be the student in a college.
According to the question:
There are 19 times as many students as professors.
We have to write an equation to show the given relationship between professors and students.
The above situation is the situation that represents the given relationship.
Answer:
(a) P (X = 6) = 0.12214, P (X ≥ 6) = 0.8088, P (X ≥ 10) = 0.2834.
(b) The expected value of the number of small aircraft that arrive during a 90-min period is 12 and standard deviation is 3.464.
(c) P (X ≥ 20) = 0.5298 and P (X ≤ 10) = 0.0108.
Step-by-step explanation:
Let the random variable <em>X</em> = number of aircraft arrive at a certain airport during 1-hour period.
The arrival rate is, <em>λ</em>t = 8 per hour.
(a)
For <em>t</em> = 1 the average number of aircraft arrival is:
The probability distribution of a Poisson distribution is:
Compute the value of P (X = 6) as follows:
Thus, the probability that exactly 6 small aircraft arrive during a 1-hour period is 0.12214.
Compute the value of P (X ≥ 6) as follows:
Thus, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8088.
Compute the value of P (X ≥ 10) as follows:
Thus, the probability that at least 10 small aircraft arrive during a 1-hour period is 0.2834.
(b)
For <em>t</em> = 90 minutes = 1.5 hour, the value of <em>λ</em>, the average number of aircraft arrival is:
The expected value of the number of small aircraft that arrive during a 90-min period is 12.
The standard deviation is:
The standard deviation of the number of small aircraft that arrive during a 90-min period is 3.464.
(c)
For <em>t</em> = 2.5 the value of <em>λ</em>, the average number of aircraft arrival is:
Compute the value of P (X ≥ 20) as follows:
Thus, the probability that at least 20 small aircraft arrive during a 2.5-hour period is 0.5298.
Compute the value of P (X ≤ 10) as follows:
Thus, the probability that at most 10 small aircraft arrive during a 2.5-hour period is 0.0108.