Page 203 - Engineering Mathematics Workbook_Final

Probability & Statistics

POSITION DISTRIBUTION 249. Suppose p is the number of cars per
minute passing through a certain road
246. The number of accidents occurring in junction between 5 PM and 6 PM,
a plant in a month follows Poisson and p has aPoisson distribution with
distribution with mean as 5.2. The mean 3. What is the probability of

probability of occurrence of less than observing fewer than 3 cars during
2 accidents in the plant during a any given minute in this interval?
randomly selected month is
3
3
9/ 2e
8/ 2e
(a) ( ) (b) ( )
(a) 0.029 (b) 0.034
( )
(c) 0.039 (d) 0.044 (c) ( ) (d) 26/ 2e
3
3
17/ 2e
[GATE, ME ; 2014 (SET-4)]
[GATE-2013 (CS)]
247. It is estimated that the average
number of events during a year is 250. An observer counts 240 veh/h at a
three. What is the probability of specific highway location. Assume
occurrence of not more than two that the vehicles arrival at the
events over a two year duration location is Poisson distributed, the
Assume that the number of events probability of having one vehicle

follow a Poisson distribution arriving over a 30-second time
interval is_____.
(a) 0.052 (b) 0.02
[GATE-2014 (CE-SET 2)]
(c) 0.072 (d) 0.002
251. The second moment of a Poisson-
[GATE, PI : 2011] distributed random variable is 2. The
mean of the random variable is
248. A manufacturer knows that eh _______. [GATE-2016]
condensers he makes contain on an
average 1% defectives. He packs 252. Vehicles arriving at an intersection

them, in boxes of 100, What is the from one of the approach roads
probability that a box picked up at follow the Poisson distribution. The
random will contain 3 or more faulty mean rate of arrival is 900 vehicles
condensers per hour. If a gap is defined as the
time difference between two
3 5
−
−
1
1
(a) 1− e (b) 1− e successive vehicle arrivals (with
2 2 vehicles assumed to be points), the
2 5 probability (up to four decimal
(c) 1− (d) 1− places) that the gap is greater than 8
e e
seconds is ____.
[GATE]
[GATE-2017 CE SESSION-I]

201