In a binomial distribution the probability of getting success is 1/4 And standard deviation is 3 then its mean is ? Option 1: 6 Option 2: 9 Option 3: 12 Option 4: 10

Answer: 12. Solution: For binomial distribution: ^2 = npq = 9, so npq = 9. With p = 1/4, q = 3/4: n x 3/16 = 9 n = 48. Mean = np = 48 x 1/4 = 12.

Applied Mathematics

Probability Distribution

Medium

In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?

✅ Correct Option: 3

For binomial distribution: $\sigma^2 = npq = 9$ , so $npq = 9$ . With $p = \frac{1}{4}$ , $q = \frac{3}{4}$ : $n \times \frac{3}{16} = 9 \Rightarrow n = 48$ . Mean $= np = 48 \times \frac{1}{4} = 12$ .

2026: 21 May Shift 2

The random variable X has a probability distribution $P(X)$ of the following form, where $k$ is some real number.

$P(X=x) = \begin{cases}k, & \text{if } x=0\\\dfrac{k}{2}, & \text{if } x=1 \text{ or } 2\\0, & \text{otherwise}\end{cases}$

On the basis of the above information, match List-I with List-II

LIST-I		LIST-II
A. Value of $k$		I. $\dfrac{1}{4}$
B. $P(X<2)$		II. 0
C. $P(X>1)$		III. $\dfrac{1}{2}$
D. $P(X>2)$		IV. $\dfrac{3}{4}$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. The variance of a Poisson distribution with mean $\lambda$ is	I. $\sqrt{\lambda}$
B. The standard deviation of a Poisson distribution with mean $\lambda$ is	II. 4
C. In a Poisson distribution, if mean is 4, then the standard deviation is	III. $\lambda$
D. In a Poisson distribution, if mean is 4, then the variance is	IV. 2

Choose the correct answer from the options given below:

2023: 15 June Shift 2

A discrete random variable X has the following probability distribution :

X:	0	1	2	3	4	5
P(X):	b	3b	5b	3b	4b	6b

The value of b is :

2023: 23 May Shift 3

A shopkeeper wants to check the average number of cars sold per call. Past record of sales is shown below:

Sale of cars (Units)	0	1	2	3
Probabilities	$\frac{1}{6}$	$\frac{1}{2}$	$\frac{3}{10}$	$\frac{1}{30}$

The expected number of cars sold is :

2026: 22 May Shift 2

The probability that a man aged 35 years will die before reaching the age of 40 years may be taken as 0.018. Out of a group of 100 men, now aged 35 years, what is the approximate probability that one man will die within next five years?

(Given: $e^{-1.8}=0.1653$ )

2023: 22 May Shift 3

If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$ , then $P(X \leq 9)$ is :

In a binomial distribution the probability of getting success is 14\frac{1}{4}41​ And standard deviation is 3 then its mean is ?

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CUET Mathematics Past Year Questions (Topic-Wise)

In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?