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 $${{31} \over {32}}$$, then p lies in the interval
  • $$\left[ {{{11} \over {12}},1} \right]$$
  • $$\left[ {{1 \over 2},{3 \over 4}} \right]$$
  • $$\left[ {{3 \over 4},{{11} \over {12}}} \right]$$
  • $$\left[ {0,{1 \over 2}} \right]$$
If the mean of Poisson distribution is $$\displaystyle \frac{1}{2}$$, 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 $$ \displaystyle P\left ( X\geq 1 \right ) $$ is
  • $$ \displaystyle \frac{2}{3} $$
  • $$ \displaystyle \frac{7}{8} $$
  • $$ \displaystyle \frac{4}{5} $$
  • $$ \displaystyle \frac{15}{16} $$
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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