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CBSE Questions for Class 12 Commerce Applied Mathematics Standard Probability Distributions Quiz 1 - MCQExams.com

Consider 5 independent bernoulli's trials each with probability p of success. If the probability of one failure is greater than or equal to 3132, then p lies in the interval
  • [1112,1]
  • [12,34]
  • [34,1112]
  • [0,12]
If the mean of Poisson distribution is 12, then the ratio of P(X=3) to P(X=2) is 
  • 1:2
  • 1:4
  • 1:6
  • 1:8
Mean and variance of binomial variable X are 2 and 1 respectively, then P(X1) is
  • 23
  • 78
  • 45
  • 1516
If for a BD the mean is 6 and standard deviation is \dfrac{1}{\sqrt{2}}, then the probability of success is
  • \dfrac{11}{12}
  • \dfrac{10}{12}
  • \dfrac{9}{12}
  • \dfrac{8}{12}
In a B.D. n = 400, P=\displaystyle \frac{1}{5}. Its standard deviation is
  • 10\times\sqrt{2}
  • \displaystyle \frac{1}{800}
  • 4
  • 8
In 15 throws of a die 4 or 5 is considered to be a success. The mean number of success is
  • 3
  • 4
  • 5
  • 6
Suppose X follows binomial distribution with parameters n = 100 and p=\dfrac{1}{3} then P(x=r) is maximum when r =
  • 49
  • 50
  • 33
  • 34
If the mean of binomial distribution is \mu , then the variance lies in the interval
  • [\mu , 0 ]
  • [0,\displaystyle \frac { \mu }{ 2 } ]
  • \left [ 0,\mu \right ]
  • \left [ 0,\sqrt{\mu } \right ]
If the first two terms of a Poisson distribution are equal to k, find k.
  • e
  • \displaystyle \frac{1}{e}
  • 1
  • 2
If the probability of selecting a bolt from 400 bolts is 0.1, then the mean for the distribution is ________
  • 0.09
  • 40
  • 36
  • 360
The value of B\left ( 3,4 ,\displaystyle \frac{1}{4}\right ) is
  • \dfrac{5}{64}
  • \dfrac{1}{16}
  • \dfrac{3}{64}
  • \dfrac{1}{64}
Given that X\sim B (n = 10, p). If E(X) = 8, then the value of p is
  • 0.6
  • 0.7
  • 0.8
  • 0.4
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is: 
  • \displaystyle \dfrac{37}{256}
  • \displaystyle \dfrac{219}{256}
  • \displaystyle \dfrac{128}{256}
  • \displaystyle \dfrac{28}{256}
Consider 5 independent Bernoulli trials each with probability of success \mathrm{p}. If the probability of at least one failure is greater than or equal to \displaystyle \frac{31}{32}, then \mathrm{p} lies in the interval. 

  • (\displaystyle \frac{1}{2}\frac{3}{4}]
  • (\displaystyle \frac{3}{4}\frac{11}{12}]
  • [0,\displaystyle \frac{1}{2}]
  • (\displaystyle \frac{11}{12},1]
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is.
  • \displaystyle\frac{63}{64}
  • \displaystyle\frac{1}{2}
  • \displaystyle\frac{127}{128}
  • \displaystyle\frac{255}{256}
A random variable X has Poisson distribution with meanThen P (x> 1.5) equals
  • \cfrac{2}{e^{2}}
  • 0
  • 1-\cfrac{3}{e^{2}}
  • \cfrac{3}{e^{2}}
A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is-
  • \dfrac{1}{729}
  • \dfrac{8}{9}
  • \dfrac{8}{729}
  • \dfrac{8}{243}
In a binomial distribution \mathrm{B} (n,p =\displaystyle \dfrac{1}{4}), if the probability of at least one success is greater than or equal to \displaystyle \dfrac{9}{10} , then \mathrm{n} is greater than 

  • \displaystyle \dfrac{1}{\log_{10}{4}-\log_{10}{3}}
  • \displaystyle \dfrac{1}{\log_{10}{4}+\log_{10}{3}}
  • \displaystyle \dfrac{9}{\log_{10}{4}-\log_{10}{3}}
  • \displaystyle \dfrac{4}{\log_{10}{4}-\log_{10}{3}}
If X has a binomial distribution, B(n, p) with parameters n and p such that P(X=2)=P(X=3), then E(X), the mean of variable X, is :
  • 3-p
  • \dfrac {p}{2}
  • \dfrac {p}{3}
  • 2-p
If the mean and the variance of a binomial variate X are 2 and 1 respectively, then probability that X takes a value greater than or equal to one is
  • \displaystyle \frac{1}{16}
  • \displaystyle \frac{9}{16}
  • \displaystyle \frac{3}{4}
  • \displaystyle \frac{15}{16}
The mean of a binomial distribution is 5, then its variance has to be :
  • > 5
  • = 5
  • < 5
  • = 25
If in a binomial distribution n=4,P(X=0)=\cfrac { 16 }{ 81 } , then P(X=4) equals
  • \cfrac { 1 }{ 16 }
  • \cfrac { 1 }{ 81 }
  • \cfrac { 1 }{ 27 }
  • \cfrac { 1 }{ 8 }
For a binomial distribution n = 20,\ q = 0.75. The mean of the distribution is
  • 10
  • 15
  • 5
  • 20
If the mean of P.D. is 5, then the variance of the same distribution is
  • 25
  • 10
  • 5
  • 15
If a random variable X follows Bernoulli Distribution with mean 2.4 and variance 1.44, the number of independent trials n is
  • 10
  • 8
  • 6
  • 2
In a binomial distribution AM=3, variance=4. The statement is
  • True
  • False
  • We cannot say
  • None
A symmetrical die is tossed twice. Getting a four is considered to be a success. The mean and variance of number of successes are
  • \cfrac { 2 }{ 3 } ,\ \cfrac { 5 }{ 18 }
  • \cfrac { 1 }{ 3 } ,\ \cfrac { 5 }{ 18 }
  • \cfrac { 1 }{ 3 } ,\ \cfrac { 7 }{ 18 }
  • \cfrac { 2 }{ 3 } ,\ \cfrac { 7 }{ 18 }
The parameter \lambda  of poisson distribution is always
  • zero
  • 1
  • -1
  • a finite positive value
The number of parameters of B.D. are
  • 4
  • 3
  • 2
  • 1

 lf the mean is \lambda and the variance is \sigma^{2} in a Poisson distribution, then
  • \displaystyle \lambda=\frac{1}{2}\sigma^{2}
  • \displaystyle \sigma^{2}=\frac{1}{2}\lambda
  • \lambda=\sigma^{2}
  • \sigma^{2}=\lambda^{2}
If {\overline{x}} and \sigma^{2} are mean and variance of poisson distribution, then
  • \overline{x}>\sigma^{2}
  • \overline{x}<\sigma^{2}
  • \overline{x}=\sigma^{2}
  • \overline{x}+\sigma^{2}=1
The S.D. of poisson distribuition whose mean is \lambda  is
  • \lambda
  • \sqrt{\lambda}
  • \lambda^{2}
  • \displaystyle \frac{1}{\sqrt{\lambda}}
The mean of a B.D, is 15 and standard deviation is 5, then which one of the following is correct.
  • \displaystyle p=\frac{2}{3}
  • \displaystyle q=\frac{5}{3}
  • data's are absolutely correct
  • data's are absolutely wrong
In a poisson distribution, the probability of 0 success is 10%. The mean of the distribution is equal to
  • \log_{10}e
  • \log_{e}10
  • 0
  • \dfrac{1}{10}
The probability that a student is not a swimmer is \frac{1}{5}. Then the probability that out of the five students, four are swimmers, is
  • ^{5}C_{4}(\frac{4}{5})^{2}(\frac{1}{2})
  • (\frac{4}{5})^{4}(\frac{1}{5})
  • ^{5}C_{1}(\frac{1}{5})(\frac{4}{5})^{4}
  • None of these
The probability that a student is not a swimmer is \displaystyle \frac{1}{5}. Then the probability that out of five students, four are swimmers is
  • \displaystyle ^{5}C_{4}\left ( \frac{4}{5} \right )^{4}\frac{1}{5}
  • \displaystyle \left ( \frac{4}{5} \right )^{4}\frac{1}{5}
  • \displaystyle ^{5}C_{1} \frac{1}{5}\left ( \frac{4}{5} \right )^{4}
  • none of these.
The standard deviation of P.D. is 1.5, then its mean is
  • 1.5
  • 2
  • 2.25
  • 3.25
If the mean of poisson distribution is 16, then its S.D. is
  • 16
  • 4
  • 10
  • 15
If X is a poisson variable with parameter 0.09,then its S.D. is
  • 0.009
  • 0.3
  • 0.03
  • 0.09
10% of tools produced by a certain manufacturing process turn out to be defective. Assuming binomial distribution, the probability of 2 defective in simple of 10 tools chosen at random, is
  • 0.368
  • 0.194
  • 0.271
  • None of these
A die is thrown 100 times, getting an even number is considered a success. Variance of number of successe, is 
  • 10
  • 20
  • 25
  • 50
In 16 throws of a die getting an even number is considered a success, then the variance of the success is
  • 4
  • 6
  • 2
  • 256
Which one of the following may be the parameter of a binomial distribution?
  • np=2, npq = 4
  • n=4, p = \dfrac{3}{2}
  • n=8, p=1
  • np=10, npq = 8
In a binomial distribution, the occurrence and the non-occurrence of an event are equally likely and the mean is 6. The number of trials required is
  • 15
  • 12
  • 10
  • 6
Let X\sim B(n,p), if

E(X)=5,Var(X)=2.5, then P(X< 1)=...................
  • { \left( \cfrac { 1 }{ 2 } \right) }^{ 11 }
  • { \left( \cfrac { 1 }{ 2 } \right) }^{ 10 }
  • { \left( \cfrac { 1 }{ 2 } \right) }^{ 6 }
  • { \left( \cfrac { 1 }{ 2 } \right) }^{ 9 }
If X is a binomial variate with the range {0,1,2,3,4,5,6} and P(X=2)=4P(X=4), then the parameter p of X is :
  • 1/3
  • 1/2
  • 2/3
  • 3/4
A coin is tossed 6 times, find the probability of getting no tails.
  • \dfrac{1}{64}
  • \dfrac{5}{64}
  • \dfrac{1}{32}
  • 0.25
Four cards are drawn from a deck of 52 cards, the probability of only two cards being spade is...... 
  • \dfrac{27}{128}
  • \dfrac{54}{128}
  • \dfrac{81}{128}
  • \dfrac{31}{128}
Four cards are drawn from a deck of 52 cards, the probability of only 1 card being spade is:
  • \dfrac{108}{256}
  • \dfrac{54}{128}
  • \dfrac{81}{256}
  • \dfrac{31}{256}
If the mean and variance of a binomial variable X are 2 and 1 respectively, then P\left( {X \geq 1} \right) =
  • \dfrac{2}{3}
  • \dfrac{15}{16}
  • \dfrac{7}{8}
  • \dfrac{4}{5}
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers