Applied Mathematics

Probability Distribution

Medium

applied

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$ ]

0.2700

0.1350

0.1804

0.2800

✅ Correct Option: 3

Here $\lambda=np=2000\times0.001=2$ . Then $P(3)=\frac{e^{-2}2^3}{3!}=\frac{0.1353\times8}{6}\approx0.1804$ .

2023: 11 Aug Shift 1

$P(X = x) = \begin{cases} 2k & \text{if } x = 0 \\ kx & \text{if } x = 1 \\ k(x - 1) & \text{if } x = 2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The value of k is

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:

2026: 29 May Shift 2

The probability distribution of a discrete random variable is given below :

X	1	2	3	4	5
P(X)	1/5	m	2/5	2m	3m

Which of the following are correct?

A. $P(2)=\frac{1}{15}$

B. $P(4)=\frac{2}{15}$

C. $P(X<2)=\frac{1}{5}$

D. $P(X\geq4)=\frac{1}{5}$

Choose the correct answer from the options given below:

2024: 16 May Shift 1

$X$	-2	-1	0	1	2
$P(X)$	$0.2$	$0.1$	$0.3$	$0.2$	$0.2$

The variance of $X$ will be :

2026: 26 May Shift 2

A traffic police officer records the number of motorcycle riders that use a particular lane on a highway. He records that an average of 2.5 motorcycle riders use the lane every hour. Given that the number of motorcycles that use the particular lane follows a Poisson distribution. The probability that less than 2 motorcycle riders will use the lane within an hour will be:- (Use $e^{2.5} = 12.2$ )

2026: 25 May Shift 1

The mean and variance of a random variable $X$ having a binomial distribution are 1 and 2/3 respectively. Then,

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $P(X=0)$	I. $1/27$
B. $P(X=3)$	II. $2/9$
C. $P(X=2)$	III. $4/9$
D. $P(X=1)$	IV. $8/27$

Choose the correct answer from the options given below:

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given e−2=0.1353e^{-2} =0.1353e−2=0.1353]

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$ ]