Poisson Distribution

Q. Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

1. $8/\left(2e^3\right)$
2. $9/\left(2e^3\right)$
3. $17/\left(2e^3\right)$
4. $26/\left(2e^3\right)$

Q. What is the probability that at most 5 defective fuses will be found in a box of 200 fuses, if 2% of such fuses are defective?

1. 0.82
2. 0.79
3. 0.59
4. 0.82

Q.

The arrival of customers over fixed time intervals in a bank follow a poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 m minutes is (correct to two decimal places).

1. 0.38

Q. The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is

1. 0.029
2. 0.034
3. 0.039
4. 0.044

Q. If a random variable X satisfies the Poisson's distribution with a mean value of 2, then the probability that X > 2 is

1. $2e^{-2}$
2. $1-2e^{-2}$
3. $3e^{-2}$
4. $1-3e^{-2}$

Q.

An observer counts 240 veh/h at a specific highway location. Assume that the vehicles arrival at the location is Poisson distributed, the probability of having one vehicle arriving over a 30-second time interval is _______.

1. 0.27

Q.

The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is .

1. 1

Q.

Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds is

1. 0.1353

Q. It is estimated that the average number of events during a year is three. What is the probability of occurrence of not more than two events over a two-year duration? Assume that the number of evets follow a poisson distribution.

1. 0.052
2. 0.062
3. 0.072
4. 0.082

Q.

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is $0.267$. Suppose you sit on a bench in a mall and observe peoples habits as they sneeze.

Complete parts $\left(a\right)$ through $\left(c\right)$.

$\left(b\right)$ What is the probability that among $12$ randomly observed individuals, fewer than $5$ do not cover their mouth when sneezing?

Using the binomial distribution, the probability is $1$. (Round to four decimal places as needed.)

Q. Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $\mu .$ The standard deviation for this distribution is given by

1. $\sqrt{\mu }$
2. ${\mu }^2$
3. $\mu$
4. $1/\mu$

Q. If calls arrie at a telephone exchange such that the time of interval of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be

1. Poisson
2. Gaussian
3. Exponential
4. Gamma

Q.

The probability of a resistor being defective is 0.02. There are 50 such aresistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is .

1. 0.26

Q.

Why is the normal distribution so important?

Q. Consider a random variable to which a Poisson distribution is best fitted. It happens that $P_{x=1}=\frac{2}{3}{P}_{x=2}$ on this distribution plot. The variance of this distribution will be

1. 3
2. 2
3. 1
4. $\frac{2}{3}$

Q.

A traffic office imposes on an average 5 number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Poisson distribution. The probability that there will be less than 4 penalties in a day is _____ .

1. 0.265

Q. A manufacturer makes condensers which on an average are 1% defective. He packs them in boxes of 100. Calculate the probability that a box picked at random will contain 3 or more faulty condensers?

1. 0.08