The number of occurrences in a given time interval or in a given space can be modeled using Poisson Distribution if the following conditions are being satisfied:
The events occur at random.
The events are independent from one another.
The average rate of occurrences is constant.
There are no simultaneous occurrences.
The Poisson distribution is defined as
$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$
where x is a discrete random variable
P(x) = probability for x occurrences μ = the mean number of occurrences
Problem
The number of cars passing a point on a road may be modelled by Poisson distribution. At an average, 4 cars enters the Caibaan Diversion Road in Tacloban City every 5 minutes. Find the probability that in a 5-minute period (a) two cars go past and (b) fewer than 3 cars go past.
Problem
A stationery store has decided to accept a large shipment of ball-point pens if an inspection of 20 randomly selected pens yields no more than two defective pens. Find the probability that this shipment is...
accepted if 5% of the total shipment is defective.
not accepted if 15% of the total shipment is defective.
Situation
A beam of uniform cross section whose flexural rigidity EI = 2.8 × 1011 N·mm2, is placed on three supports as shown. Support B is at small gap Δ so that the moment at B is zero.
Situation
A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length x is so calculated in order that the reactions at all supports shall be the same.
Problem
Divide the circle of radius 13 cm into four parts by two perpendicular chords, both 5 cm from the center. What is the area of the smallest part.