The mean and standard deviation of a binomial | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a binomial distribution, the mean is given by $\mu = np = 4$ and the variance is $\sigma^2 = npq = (\sqrt{3})^2 = 3$. Dividing the variance by

Vedclass · Accepted Answer

$1-\left(\frac{3}{4}\right)^{16}$

Vedclass · Answer

(B) For a binomial distribution, the mean is given by $\mu = np = 4$ and the variance is $\sigma^2 = npq = (\sqrt{3})^2 = 3$. Dividing the variance by the mean, we get $\frac{npq}{np} = \frac{3}{4}$, which implies $q = \frac{3}{4}$. Since $p + q = 1$, we have $p = 1 - \frac{3}{4} = \frac{1}{4}$. Substituting $p = \frac{1}{4}$ into $np = 4$, we get $n(\frac{1}{4}) = 4$, so $n = 16$. We need to find $P(X \geq 1)$. Using the complement rule, $P(X \geq 1) = 1 - P(X = 0)$. For a binomial distribution, $P(X = k) = {}^{n}C_{k} p^{k} q^{n-k}$. Thus, $P(X = 0) = {}^{16}C_{0} (\frac{1}{4})^{0} (\frac{3}{4})^{16} = 1 	imes 1 	imes (\frac{3}{4})^{16} = (\frac{3}{4})^{16}$. Therefore, $P(X \geq 1) = 1 - (\frac{3}{4})^{16}$.

The mean and standard deviation of a binomial variate $X$ are $4$ and $\sqrt{3}$ respectively. Then $P(X \geq 1)$ is equal to

Similar Questions

If the sum of the mean and the variance of a binomial distribution for $5$ trials is $1 \cdot 8$,then $p=$

The probability that a student is a singer is $\frac{1}{5}$. Then,the probability that $4$ students are singers out of $5$ students is . . . . . . .

The mean and variance of a binomial distribution are $4$ and $3$ respectively. Then,the probability of getting exactly six successes in this distribution is:

Consider $5$ independent Bernoulli trials,each with a probability of success $p$. If the probability of at least one failure is greater than or equal to $31/32$,then in which interval does $p$ lie?

$A$ binomial random variable $X$ satisfies $9 \cdot P(X=4) = P(X=2)$ when $n=6$. Then $p$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module