POISSON DISTRIBUTION (C )

        POISSON DISTRIBUTION

1) Poisson distribution is a ___ probability distribution.

A)  continuous B) discrete

C) both A and B D)neither A nor 

2) which one is uni-parametric distribution ?

A)Binomial Distribution B) normal distribution C) Poisson distribution D) geometric Distribution

3) which one is not a condition of poison Model

A) the probability of having success in a small time interval is constant.

B) the probability of having success in a small interval is independent of time and also earlier.

C)  the probability of having success more than one in a small time interval is very small. D) n

4) ____Distribution is the limiting case of Binomial Distribution.

A) normal distribution

 B) poisson distribution 

C) Chi square distribution

D) F- distribution 

5) Poisson distribution may be 

A) bimodal B) unimodal  C) multimodal  D) either A or B) above and not C.

6) ____ distribution is sometimes known as the "distribution of rare events".

A) binomial  B) normal C) geometric D) Poisson

7) In ____ distribution, mean = variance.

A) Chi square B) normal  C) poison D) hypergeometric 

8) when the number of trials is large, then the distribution used is:

A) poison distribution  B) F-distribution  C) t- Distribution D) Normal Distribution

9) For a poison distribution

 A) standard deviation and variance are equal  B) mean variance are equal C) mean and standard deviation are equal D) both A and B above.

10)  number of radioactive atoms decaying in a given interval of time is an example of

A) normal distribution B) binomial distribution C) Poisson distribution D) n

11) In Poisson distribution, probability of success is very close to:

A)1 B) 0.8 C) 0 D) none 

12) poison distribution is: 

A) always negatively skewed. B) always positively skewed C) always asymmetric D) symmetric only when m= 2 

13) the poison distribution tends to be symmetrical if the mean value is:

A) zero B) very low C) high D) n 

14)  for Poissonon fitting to an observed frequency distribution

A) we equate the poisson parameter to the mean of the frequency distribution. B)  we equate the poisson parameter to the mode of the distribution C)  we equate the poissonon parameter to the median of the distribution D) n 

15) number of misprints per page of a thick book follows: 

A) normal distribution B) poisson distribution C) standard normal distribution D) F-distribution

16) If a random variable X follows  Poisson distribution, such that P(X=1)=P(X=2), then mean of the Distribution.

A) 2     B) 4. C) 3 D) 2 

17) If a random variable X follows Poisson distribution, such that P(X=1)=P(X=2), then mean and variance are..

A) 4,4  B) 3,3  C) 2,2  D) 5,5 

18) A random variable X follows  Poisson distribution, such that P(X=k)=P(X=k+2), then mean and variance is:

A) k-1, k-1 B) k+2, k+2 C) k+3, k+3 D) k+1, k+1. 

19) For a Poisson Variate, if P(X=0)= P(X=1)= k, the value of k is 

A) e  B) 1/e. C) e² D) 1/√e E) none

20) If a random variable X follows  Poisson distribution, such that P(X=0)=P(X=1), then P(X= 2)=? 

A) e B) 1/2e. C) 2/e D) 1/e 

21) For a Poisson distribution X, if P(X=0)= 0.2, then the variance of the Distribution is: 

A) log 2 B) log 4 C) log 5 D) none 

22) The mean of a Poisson Distribution is 0.5, then ratio of P(X=3) to P(X=2) is ? 

A) 1:6  B) 6:1  C) 1:3  D) 2:5 

23) For a Poisson variate X, P(X=2)= 3P(X=3), then the mean of X is: 

A) 0.50 B) 0.33 C) 1.00 D) 0.25 

24) If X is a Poisson Variate withP(X=0)= 0.80, then variance is 

A) log 10 B) log(5/4) C) log e D) n 

** A random variable X follows Poisson distribution with parameter 4. Find the probability (given e⁻⁴=0.0183)

25) P(X=0) 

A) 0.0183 B)0.15616 C)0.1952 D) n 

26) P(X=1) 

A)0.1464 B)0.0732 C)0.3725 D) n 

27) P(X=2) 

A) 0.3752 B) 0.0732 C) 0.1464 D) n 

28) P(X=3) 

A) 0.1952 B)0.1529 C)0.1295 D) 0.2052

29) P(X=4) 

A) 0.5219 B) 0.1952 C) 0.2952 D) 0.3952 

30) P(X=5) 

A) 0.15616 B) 0.16516 C) 0.26514 D) 0.21569 

31) P(X<2) 

A) 0.1595 B) 0.0915 C) 0.1554 D) 0.0947

32) P(X is atleast 3) 

A) 0.7621 B) 0.2671 C) 0.6721 D) n 

33) P(X is almost 2) 

A) 0.3297 B) 0.2549 C) 0.2379 D) N 

34) P(X is more than 3) 

A) 0.6659 B)0.5596 C) 0.5779 D) 0.4081 

35) P(X is 2 or more than 2) 

A) 0.2497 B) 0.4296 C) 0.4081 D) 0.7259 

36) P(3 <X<5) 

A) 0.5219 B) 0.1952 C) 0.2954 D) 0.3459 

37) P(3≤ X<5) 

A) 0.3904 B) 0.2904 C) 0.1904 D) 0.0904 

38) P(3<X<5) 

A) 0.3595 B) 0.3513 C) 0.4513 D) 0.2549 

39) (3 ≤ X≤5) 

A) 0.5987 B) 0.4598 C) 0.4665 D) 0.5465 

40) The standard Deviation of the given Poisson distribution is ? 

A) 1   B) 2     C) 3    D) 4 

41) For a Poisson distribution mean is 10, standard Deviation is 5 find the point of fallacy.

A) The given statement has no fallacy B) If mean of the distribution is 10, standard deviation should be 3 C) If Standard deviation is 5, then mean of the Distribution should be 25. E) none

**** If 3% of the bolts manufactured by the company are defective. What is the probability that is a sample at 200 bolts.         (e⁻⁶= 0.00248)

42) 5 bolts will be defective ? 

A) 0.611 B) 0.15 C) 0.160 D)0.258 

43) None is defective ? 

A) 0.00248 B) 0.00496 C) 0.00124 D) none 

44) The variance of a Poisson distribution is 4. Find the probability x=3        (e⁻⁴=0.0183)

A)0.1965 B)0.1952 C)0.1925 D)0.2519

45) The standard Deviation of a Poisson Variate is √3. Find the probability that x=2   (e⁻³=0.0498) 

A)0.2241 B) 0.1422 C)0.2142 D) 0.2214 

46) The standard Deviation of a Poisson Variate is 2. Find the probability that x=2.   (e⁻⁴= 0.0183) 

A)0.1646 B)0.1596 C) 0.1446 D)0.1464 

** If the probability that an individual suffers a bad reaction from a particular injection is 0.01. find the probability that out of 500 individuals:.     (e⁻⁵= 0.00674)

47) Exactly two will suffer from bad reaction ? 

A)0.08425 B) 0.09425 C) 0.12549 D) none 

48) More than 2 individuals will suffer a bad reaction. 

A) 0.87995 B) 0.87551 C) 0.85229 D) none 

49) In a company manufacturing toys. It is found that 1 in 500 is defective. Find the probability that there will be at most two defective in a sample of 2000 units.  (e⁻⁴= 0.0183) 

A)0.2597 B)0.3549 C)0.2549 C)0.2379 

50) If 2% of the items made by a factory are defective. Find the probability that the there are 3 defective items in a sample of 100 items. 

A) 0.190 B)0.154 C)0.180 D) none 

*** Experience has shown that, as the average, 2% of the airline's flights suffer a minor equipment failure in an aircraft. Estimate the probability that the number of minor equipment failure in the next 50 flights will be :

51) 0(zero) 

A) 0.3879 B)0.1498 C)0.3598 D)n 

52) atleast 2(Two). 

A)0.2224 B)0.4424 C)0.2242 D) N 

*** Between 4 and 5 P. M, the average number of phone calls per minute coming in to the switchboard of the company 3. Find the probability that in one particular minute there will be ? (e⁻³= 0.498) 

53)No phone call.

A) 0.0498 B)0.0598 C)0.4598 D) 0.4587 

54) Exactly 2 phone calls.

A)0.1422 B)0.2214 C)0.2251 D)0.2241

55) Between the hours 2 p.m. and 4 p.m. the average number of phone calls coming into the switch board of the company is 2.35. find the probability that in a particular minute there will be at most 2 phone calls (e⁻²•³⁵= 0.095374)

A) 0.582854 B) 0.584987 C) 0.549875 D) none 

56) Assume that 4% of the output of the factory making certain parts is defective and that 100 units.are in package, what is the probability that almost 3 defective parts may be found in package. ((e⁻⁴= 0.0183) 

A)0.4331 B)0.3341 C)0.3314 D) n 

** is found that the number of accidents in a factory follows poisson distribution with a mean of two accidents for week (e⁻²=0.135) 

57) find the probability that no accident occurs in a week 

A)0.531 B)0.315 C)0.135 D) n 

58) find the probability that the number of accident in a week exceeds 2. 

A)0.325 B)0.523 C)0.352 D) none 

*** The number of accidents attributed in a year to the taxi drivers in a city follows poisson distribution with mean 3. Out of 1000 taxi drivers, find approximately (e⁻¹= 0.3879,e⁻²= 0.1353, e⁻³= 0.0498) 

59) the number of taxi driver with no accident in a year. 

A) 45    B) 60   C) 50    D) 75 

60) the number of taxi drivers with more than 3 accidents in a year. 

A) 303 B) 353 C) 453 D) 403 

61) the average number of misprints per page of a book is 1.5.  what is the probability that a particular page is free from  misprints? 

A)0.12    B) 0.22. C) 0.32 D) none 

62) taking data from the previous questions; if the book contains 800 pages. how many of these contain more than one misprint?(e⁻¹= 0.22) 

A) 303 B) 353 C) 360 D) 460 

63) If the chance of being killed by flood during a year is 1/3000, use poisson distribution to calculate the probability that out of 3000 persons living in a village at least one would die in a flood in a year 

A) e⁻¹  B) e  C) 1 - e⁻¹  D) none 

64) A radioactive source emits on the averaged 2.5 particles per second. calculate the two or more particles will be emitted in an interval of four seconds. 

A) 11e⁻¹⁰ B)1- 10e⁻¹⁰C)1-11e⁻¹⁰ D) n

65) In turning out certain toys in a manufacturing process in a factory, the average number of defective is 10%. What is the probability that exactly three defectives in a sample of 10 toys chosen at random, by using Poissonon approximation to the Binomial Distribution(e= 2.72)

A)0.041 B)0.051 C)0.031 D)0.061

*** 1/5% of the blades produced by a blade manufacturing factory turn out to be defective. the blades are supplied in a packet of 10.  use poisson distribution to calculate the number of packets in a consignment of 100000 packets. (11e⁻⁰•⁰²= 0.9802)

66) containing no defective.

A) 97580 B) 98020 C) 98000 D) 99020 

67) containing one defective. 

A)1900 B) 1978 C)1987 D)1960 

68) containing 2 defectives 

A)15  B) 20   C) 25   D) 35 

69) A manufacture of blades knows that 5% of the product is defective. If he sells blades in boxes of 100 and guarantees that not more than 10 blades will be defective. what is  probability (approximately) that a box will fail to meet the guaranteed quantity ?

A) 1 - e⁻⁵  B) e⁻⁵[1+ 5/1! + 5²/2! + 5³/3! +.....+5¹⁰/10!]  C) 1 -e⁻⁵[1+ 5/1! + 5²/2! + 5³/3!+.....+5¹⁰/10!] D) n

70) A local electric appliance has found from experience the demand for the tubelight is distributes as Poisson distribution with a mean of 4 tubelight per week. If the shop keeps 6 tubes during a particular week what is the probability that the demand will exile the supply during that week ? (e⁻⁴= 0.0183)

A)0.1114 B)0.2224 C)0.1525 D)0.1254 

*** Number of road accidents in a highway during a month follows the poisson distribution with mean 6. Find the probability that in a certain month number of accident will be (e⁻⁶= 0.00248)

71) not more than three.

A)0.15248 B)0.15128 C)0.15498 D)0.25149 

72) between 2 and 4. 

A) 0.08901 B)0.09928 C)0.08928 D) n 

*** A manufacturer who produces medicine bottles, find that 0.1% bottles are defective. the bottles are packed in boxes containing 500 bottles. A drug manufacturer buys 100 boxes from the producers of bottles. using poisson distribution find how many boxes will contain (e⁻⁰•⁵= 0.6065)

73) no defectives

A) 40  B) 50 C) 69 D) 61

74) at least two defectives.

A) 8    B) 9     C) 10    D) 15 

75) the probability that a poisson variate x takes a positive value (1 - e⁻¹•⁵). Find the variance and also the probability that x lies between -1.5 and 1.5.

A)1.5, 2.5/e B) 1.5, 2.5/e¹•⁵ C) 1.5, 1.5 D) none 

76) In a certain factory blades are manufactured in packets of 10. There is a 0.2% probability that for any blade to be defective. using poisson distribution calculate the number of packets containing two defective blades in a consignment of 20000 packets. (e⁻⁰•⁰²= 0.9802)

A) 2   B) 4   C) 8     D) 16 

77) A certain Hospital usually admits patients per day. On an average 4 patients in 100 require special facilities found in special rooms of the hospital. On the morning of certain days it is found that there are 4 such rooms available. Assuming that 50 patients will be admitted, find the probability that more than 4 patients will require such special rooms.(e⁻²= 0.13534)

A)0.02525 B) 0.05226 C)0.05262 D) n 

78) If X is a Poisson variable such that P(X=2)= 9P(X=4)+ 90P(X=6),  find the mean and variance of X.

A) 2.   B) 3.   C) 1   d) 4