Advertisements
Advertisements
प्रश्न
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
उत्तर
Given that mean, i.e. np = 20 ...(1)
and standard deviation, i.e. npq = 4
\[\sqrt{npq} = 4 \]
\[ \Rightarrow npq = 16 . . . (2)\]
\[\text{ Dividing eq (2) by eq (1), we get } \]
\[q = \frac{16}{20} = \frac{4}{5}\]
\[\text{ and } p = \frac{1}{5}; \]
\[ \therefore n = \frac{Mean}{p} = 100 \]
\[P(X = r) = ^{100}{}{C}_r \left( \frac{1}{5} \right)^r \left( \frac{4}{5} \right)^{100 - r} , r = 0, 1, 2 . . . . . 100\]
\[\text{ Therefore, the parameters are n = 100 and p } = \frac{1}{5}\]
APPEARS IN
संबंधित प्रश्न
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
- all the five cards are spades?
- only 3 cards are spades?
- none is a spade?
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(A) 10−1
(B) `(1/2)^5`
(C) `(9/10)^5`
(D) 9/10
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
A box contains 100 tickets, each bearing one of the numbers from 1 to 100. If 5 tickets are drawn successively with replacement from the box, find the probability that all the tickets bear numbers divisible by 10.
In a large bulk of items, 5 percent of the items are defective. What is the probability that a sample of 10 items will include not more than one defective item?
A bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one with replacement, what is the probability that one is red?
Find the probability distribution of the number of sixes in three tosses of a die.
Six coins are tossed simultaneously. Find the probability of getting
(i) 3 heads
(ii) no heads
(iii) at least one head
An experiment succeeds twice as often as it fails. Find the probability that in the next 6 trials there will be at least 4 successes.
In a multiple-choice examination with three possible answers for each of the five questions out of which only one is correct, what is the probability that a candidate would get four or more correct answers just by guessing?
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8.
If X follows a binomial distribution with mean 4 and variance 2, find P (X ≥ 5).
If the sum of the mean and variance of a binomial distribution for 6 trials is \[\frac{10}{3},\] find the distribution.
If in a binomial distribution n = 4 and P (X = 0) = \[\frac{16}{81}\] , find q.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
If in a binomial distribution n = 4, P (X = 0) = \[\frac{16}{81}\], then P (X = 4) equals
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire in order to have more than 50% chance of hitting it at least once is
Let X denote the number of times heads occur in n tosses of a fair coin. If P (X = 4), P (X= 5) and P (X = 6) are in AP, the value of n is
One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw is
If the mean and variance of a binomial distribution are 4 and 3, respectively, the probability of getting exactly six successes in this distribution is
Mark the correct alternative in the following question:
A box contains 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
Mark the correct alternative in the following question:
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\] is independent of n and r, then p equals
Mark the correct alternative in the following question:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is
Mark the correct alternative in the following question:
Which one is not a requirement of a binomial dstribution?
A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that all are white ?
For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p
One of the condition of Bernoulli trials is that the trials are independent of each other.
If the coefficients of x7 and x8 in `(2 + x/3)^n` are equal, then n is
If a fair coin is tossed 10 times. Find the probability of getting at most six heads.
A fair coin is tossed 8 times. Find the probability that it shows heads at most once.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.
