Advertisements
Advertisements
Question
Determine the binomial distribution whose mean is 20 and variance 16.
Solution
Mean, i.e. np =20 ....(1)
Variance, i.e. npq =16 ....(2)
\[\text{ Dividing eq (2) by eq (1), we get } \]
\[\frac{npq}{np} = \frac{16}{20}\]
\[ \Rightarrow q = \frac{4}{5}\]
\[ \Rightarrow p = 1 - q \]
\[ \therefore p = \frac{1}{5} \]
\[\text{ As np } = 20 \]
\[ \Rightarrow n = 100\]
\[ \therefore P(X = r) = ^{100}{}{C}_r \left( \frac{1}{5} \right)^r \left( \frac{4}{5} \right)^{100 - r} , r = 0, 1, 2 . . . . 100\]
APPEARS IN
RELATED QUESTIONS
The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
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
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
The probability of a man hitting a target is 1/4. If he fires 7 times, what is the probability of his hitting the target at least twice?
Eight coins are thrown simultaneously. Find the chance of obtaining at least six heads.
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?
A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.
A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.
The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is
\[\frac{28 \times 9^6}{{10}^8} .\]
The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
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.
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university only one will graduate .
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`. What is the probability that he will win a prize at least once.
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.
Can the mean of a binomial distribution be less than its variance?
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 mean and variance of a random variable X with a binomial distribution are 4 and 2 respectively, find P (X = 1).
If the mean and variance of a binomial variate X are 2 and 1 respectively, find P (X > 1).
If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
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 any two are white ?
Bernoulli distribution is a particular case of binomial distribution if n = ______
The sum of n terms of the series `1 + 2(1 + 1/n) + 3(1 + 1/n)^2 + ...` is
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
The probability of hitting a target in any shot is 0.2. If 5 shots are fired, find the probability that the target will be hit at least twice.
If the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.
