If the sum of the mean and the variance of a | vedclass

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

Question

(D) For a Binomial distribution with $n$ trials,the mean is $\mu = np$ and the variance is $\sigma^2 = npq$,where $q = 1 - p$.Given $n = 5$ and $\mu +

Vedclass · Accepted Answer

$0.2$

Vedclass · Answer

(D) For a Binomial distribution with $n$ trials,the mean is $\mu = np$ and the variance is $\sigma^2 = npq$,where $q = 1 - p$.Given $n = 5$ and $\mu + \sigma^2 = 1.8$.Substituting the values,we get:$np + npq = 1.8$$5p + 5p(1 - p) = 1.8$$5p + 5p - 5p^2 = 1.8$$10p - 5p^2 = 1.8$$5p^2 - 10p + 1.8 = 0$Multiplying by $10$ to clear the decimal:$50p^2 - 100p + 18 = 0$Dividing by $2$:$25p^2 - 50p + 9 = 0$Using the quadratic formula $p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$p = \frac{50 \pm \sqrt{2500 - 4(25)(9)}}{50} = \frac{50 \pm \sqrt{2500 - 900}}{50} = \frac{50 \pm \sqrt{1600}}{50} = \frac{50 \pm 40}{50}$$p_1 = \frac{90}{50} = 1.8$ (Not possible since $0 \le p \le 1$)$p_2 = \frac{10}{50} = 0.2$Thus,$p = 0.2$.

If the sum of the mean and the variance of a Binomial distribution for $5$ trials is $1.8$,then the value of $p$ is

Similar Questions

$A$ fair die is thrown up to $20$ times. The probability that on the $10^{th}$ throw,the fourth six appears is:

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least $0.96$ is:

$A$ fair die with faces $1, 2, 3, 4, 5,$ and $6$ is tossed $4$ times. What is the probability that in all $4$ tosses,the value obtained is not less than $2$ and not greater than $5$ (in $/81$)?

If $A$ and $B$ throw two dice $100$ times each simultaneously,then the probability that both of them will get an even number as the total score at the same time in all the throws is

An experiment succeeds twice as often as it fails. The probability of at least $5$ successes in the $6$ trials of this experiment is

Vedclass Test Series

Exam Paper Generator

Online Exam Module