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Recent questions and answers in Probability Distribution
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TN XII Math
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Probability Distribution
A discrete random variable $x$ has the following probability distributioxs.Find $p(x<3)$\[\]$\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$
tnstate
class12
bookproblem
c10
sec-1
exercise10-1
p203
q4
q4-2
modelpaper
mar-2007
answered
Feb 11
by
rashi.goyal2002
1
answer
Marks in an aptitude test given to $800$ students of a school was found to be normally distributed. $10\%$ of the students scored below $40$ marks and $10\%$ of the students scored above $90$ marks. Find the number of students scored between $40$ and $90$.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q7
modelpaper
jun-2006
answered
Sep 20, 2013
by
sreemathi.v
1
answer
If the hight of $300$ students are normally distributed with mean $64.5$ inches and standard deviation $3.3$ inches,find the hight below which $99\%$ of the student lie.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q6
answered
Sep 19, 2013
by
sreemathi.v
1
answer
The mean weight of $500 $ male students in a certain college in $151$ pounds and the standard deviation is $15$ pounds. Assuming the weights are normally distributed, find how many students weigh more than $185$ pounds
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q5
q5-2
modelpaper
mar-2006
mar-2009
answered
Sep 19, 2013
by
sreemathi.v
1
answer
The mean weight of $500 $ male students in a certain college in $151$ pounds and the standard deviation is $15$ pounds. Assuming the weights are normally distributed, find how many students weigh between $120$ and $155$ pounds
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q5
q5-1
modelpaper
mar-2006
mar-2009
answered
Sep 19, 2013
by
sreemathi.v
1
answer
The life of army shoes is normally distributed with mean $8$ months and standard deviation $2$ months. If $5000$ pairs are issued, how many pairs would be expected to need replacement within $12$ months.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q4
answered
Sep 19, 2013
by
sreemathi.v
1
answer
Suppose that the amount of cosmic radiation to which a person is exposed when flying by jet across the united states is a random variable having a normal distribution with a mean of $4.35 m$ rem and standard deviation of $0.59m$ rem. What is the probability that a person will be exposed to than $5.20m$ rem of cosmic radiation of such flight.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q3
modelpaper
jun-2007
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $Z$ is a standard normal variate. Find the value of $c$ for the following $P(Z > c)=0.85$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q2
q2-3
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $Z$ is a standard normal variate. Find the value of $c$ for the following $P(-c < Z < c)=0.40$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q2
q2-2
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $Z$ is a standard normal variate. Find the value of $c$ for the following $ P(0< Z < c)=0.25$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q2
q2-1
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing.$P(85\leq$X$\leq$95$)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q1
q1-5
modelpaper
mar-2006
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilites by standardizing. $P(70$$<$X$)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q1
q1-4
modelpaper
mar-2006
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing. $P(65\leq$X$\leq$100$)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q1
q1-3
modelpaper
mar-2006
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing.$P(X\leq$80$)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q1
q1-2
modelpaper
mar-2006
answered
Sep 19, 2013
by
sreemathi.v
1
answer
If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing. $P(X\leq$100$)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-5
p228
q1
q1-1
modelpaper
mar-2006
answered
Sep 19, 2013
by
sreemathi.v
1
answer
The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$ out of $1000$ taxi drivers find approximately the number of driver with more than $3$ accidents in a year $[e^{-3}=0.0498].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q5
q5-2
modelpaper
jun-2006
oct-2008
oct-2009
answered
Sep 19, 2013
by
sreemathi.v
1
answer
The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$. Out of $1000$ taxi drivers find approximately the number of driver with no accident in a year .$[e^{-3} = 0.0498].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q5
q5-1
modelpaper
jun-2006
oct-2008
oct-2009
answered
Sep 19, 2013
by
sreemathi.v
1
answer
Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be at least $2$ emission in a particular $20$ minutes interval .$[e^{-5}=0.0067].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q4
q4-2
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be $2$ emission.$[e^{-5}=0.0067].$
tnstate
bookproblem
ch10
sec-1
exercise10-4
p219
q4
q4-1
answered
Sep 18, 2013
by
sreemathi.v
1
answer
$20\%$ of the bolts produced in a factory are found to be defective. Find the probability that in a sample of $10$ bolts chosen at random exactly $2$ will be defective using ,Poisson distribution.$ [e^{-2}=0.1353].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q3
q3-2
answered
Sep 18, 2013
by
sreemathi.v
1
answer
$20\%$ of the bolts produced in a factory are found to be defective. Find the probability that in a sample of $10$ bolts chosen at random exactly $2$ will be defective using ,Binomial distribution.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q3
q3-1
answered
Sep 18, 2013
by
sreemathi.v
1
answer
If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that more than $3$ fuses are defective$ [e^{-4}=0.0183].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q2
q2-2
answered
Sep 18, 2013
by
sreemathi.v
1
answer
If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that exactly $4$ fuses are defective
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q2
q2-1
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Let $x$ have a poisson distribution with mean $4$.Find$P(2\leq$X$<$5$)[e^{-4}=0.0183].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q1
q1-2
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Let $X$ have a poisson distribution with mean $4$.Find $(i) \;P(X\leq $3$)\qquad[e^{-4} = 0.0183].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q1
q1-1
answered
Sep 18, 2013
by
sreemathi.v
1
answer
In a hurdle race a player has to cross $10$ hurdles. The probability that he will clear each hurdle is $\large\frac{5}{6}$. What is the probability that he will knock down less than $2$ hurdles.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q6
answered
Sep 18, 2013
by
sreemathi.v
1
answer
The overall percentage of passes in a certain examination is $80$.If $6$ candidates appear in the examination what is the probability that atleast $5$ pass the examination.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q5
modelpaper
oct-2007
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Four coins are tossed simultaneously .what is the probability of getting at most two heads
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q4
q4-3
modelpaper
mar-2008
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Four coins are tossed simultaneously.what is the probability of getting at least two heads
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q4
q4-2
modelpaper
mar-2008
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Four coins are tossed simultaneously .what is the probability of getting exactly $2$ heads
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q4
q4-1
modelpaper
mar-2008
answered
Sep 18, 2013
by
sreemathi.v
1
answer
If on an average $1$ ship out of $10$ do not arrive safely to ports. Find the mean and the standard deviation of ship returning safely out of a total of $500$ ships
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q3
answered
Sep 18, 2013
by
sreemathi.v
1
answer
A die is thrown $120$ times and getting $1$ or $5$ is considered a success.Find the mean and variance of the number of successes.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q2
answered
Sep 18, 2013
by
sreemathi.v
1
answer
The mean of a binomial distribution is $6$ and its standard deviation is $3$. Is this statement true or false?comment?
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q1
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if $x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q7
q7-3
modelpaper
mar-2006
oct-2007
mar-2008
answered
Sep 18, 2013
by
sreemathi.v
1
answer
Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} \alpha e^{-\alpha x} ,& \quad \text{if $x$$>$$0$}\\ 0 ,& \quad \text{otherwise} \end{array} \right.$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q7
q7-2
modelpaper
oct-2009
answered
Sep 17, 2013
by
sreemathi.v
1
answer
Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} \frac {1}{24} ,& \quad \text{-12$\leq$$ x$$\leq $$12$}\\ 0, & \quad \text{otherwise} \end{array} \right.$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q7
q7-1
modelpaper
oct-2006
answered
Sep 17, 2013
by
sreemathi.v
1
answer
The probability distribution of a random variable $x$ is given below: \[\] $\begin{array} {llllllll} \textbf{X:}& 0& 1& 2& 3 \\ \textbf{P(X=x):}& 0.1& 0.3 &0.5& 0.1& \end{array}$\[\] If $Y=X^{2}+2X$ find the mean and variance of $Y$.
tnstate
class12
bookproblem
c10
sec-1
exercise10-2
p211
q6
modelpaper
jun-2008
answered
Sep 17, 2013
by
sreemathi.v
1
answer
In a gambling game a man wins Rs.$10 $ if he gets all heads or all tails and loses Rs.$5$ if he gets $1$ or $2$ heads when $3$ coins are tossed once. Find his expectation of gain.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q5
answered
Sep 17, 2013
by
sreemathi.v
1
answer
Two cards are drawn with replacement from a well shuffled deck of $52$ cards. Find the mean and variance for the number of aces.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q4
answered
Sep 17, 2013
by
sreemathi.v
1
answer
In an entrance examination a student has to answer all the $120$ questions. Each question has four options and only one option is correct. A student gets $1$ mark for a correct answer and loses half mark for a wrong answer. What is the expectation of the mark scored by a student if he chooses the answer to each question at random?
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q3
modelpaper
jun-2007
answered
Sep 17, 2013
by
sreemathi.v
1
answer
Find the expected value of the number on a die when thrown.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q2
answered
Sep 17, 2013
by
sreemathi.v
1
answer
A die is tossed twice. A success is getting as odd number on a toss. Find the mean and the variance of the probability distribution of the number of successes.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q1
answered
Sep 17, 2013
by
sreemathi.v
1
answer
A random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ Find $p(\large\frac{\pi}{2}<x<\frac{3\pi}{2})$
tnstate
class12
bookproblem
ch10
sec-1
p204
q10
q10-3
answered
Sep 17, 2013
by
sreemathi.v
1
answer
A random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ Find $p(0<x<\large\frac{\pi}{2})$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-1
p204
q10
q10-2
answered
Sep 17, 2013
by
sreemathi.v
1
answer
A random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{1 1} k & \quad 0 < x < 2n \\ 0 & \quad \text{else where} \end{array} \right.$ Find $k$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-1
p204
q10
q10-1
answered
Sep 17, 2013
by
sreemathi.v
1
answer
A continuous random variable $x$ has the p.d.f defined by $f(x) = \left\{ \begin{array}{1 1} ce^{-ax} & \quad 0 < x < \infty \\ 0 & \quad \text{else where} \end{array} \right.$ Find the value of $c$ if $a>0$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-1
p204
q9
answered
Sep 17, 2013
by
sreemathi.v
1
answer
For the distribution function given by $f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{$0$$\leq$$x$$\leq$$1$}\\ 1 & \quad \text{x>1} \end{array} \right.$\[\] Find the density function. Also evaluate $p(x>0.75)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-1
p204
q8
q8-3
answered
Sep 17, 2013
by
sreemathi.v
1
answer
For the distribution function given by $f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{$0$$\leq$$x$$\leq$$1$}\\ 1 & \quad \text{x>1} \end{array} \right.$\[\] Find the density function. Also evaluate $p(x\leq0.5)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-1
p204
q8
q8-2
answered
Sep 17, 2013
by
sreemathi.v
1
answer
For the distribution function given by $f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{$0$$\leq$$x$$\leq$$1$}\\ 1 & \quad \text{x>1} \end{array} \right.$\[\] Find the density function. Also evaluate p(0.5< x <0.75)
tnstate
class12
bookproblem
ch10
sec-1
exercise10-1
p204
q8-1
answered
Sep 16, 2013
by
sreemathi.v
1
answer
The probability density function of a random variable $x$ is $f(x) = \left\{ \begin{array}{l l} kx^{\alpha-1}e^{-\beta\;x^{\alpha}}, & \quad \text{x,$\alpha$$,\beta$>$0$}\\ 0 ,& \quad \text{elsewhere} \end{array} \right.$, Find $p(x$>$10)$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-1
p204
q7
q7-2
answered
Sep 16, 2013
by
sreemathi.v
1
answer
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