Face masks are supplied to a junior college i | vedclass

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

Question

(A) The probability of a mask being defective is $p = \frac{1}{500} = 0.002$. In a packet of $n = 100$ masks, the expected number of defective masks i

Vedclass · Accepted Answer

$\frac{10,000}{e^{0.2}}$

Vedclass · Answer

(A) The probability of a mask being defective is $p = \frac{1}{500} = 0.002$. In a packet of $n = 100$ masks, the expected number of defective masks is $\lambda = np = 100 	imes 0.002 = 0.2$. Using Poisson distribution, the probability that a packet contains $r$ defective masks is $P(X = r) = \frac{e^{-\lambda} \lambda^r}{r!}$. For a packet to contain no defective masks, we set $r = 0$: $P(X = 0) = \frac{e^{-0.2} (0.2)^0}{0!} = e^{-0.2}$. In a consignment of $10,000$ packets, the number of packets with no defective masks is $10,000 	imes P(X = 0) = 10,000 	imes e^{-0.2} = \frac{10,000}{e^{0.2}}$.

$X = x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$K + \frac{2}{10}$	$K + \frac{3}{10}$	$K + \frac{3}{10}$	$K + \frac{4}{10}$	$K + \frac{2}{10}$

$X = x$	$-4$	$-2$	$0$	$2$	$4$	$6$	$8$	$10$
$F(X = x)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

Face masks are supplied to a junior college in packets of $100$. If there is a chance that $1$ in $500$ face masks is defective, then the number of packets containing no defective face masks in a consignment of $10,000$ packets is:

Similar Questions

If $f(x) = \frac{x+2}{18}$ for $-2 < x < 4$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a random variable $X$,then the value of $P(|X| < 2)$ is

For the probability distribution of a discrete random variable $X$ as given below,the mean of $X$ is:
$X = x$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X = x)$ $\frac{1}{10}$ $K + \frac{2}{10}$ $K + \frac{3}{10}$ $K + \frac{3}{10}$ $K + \frac{4}{10}$ $K + \frac{2}{10}$

The cumulative distribution function of a discrete random variable $X$ is given by the following table:
$X = x$ $-4$ $-2$ $0$ $2$ $4$ $6$ $8$ $10$
$F(X = x)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,calculate $\frac{P(X \leqslant 0)}{P(X > 0)}$.

If a die is thrown at random,then the expectation of the number on it is

The probability function of a random variable $X$ is given by $P(X=k)=c k^2$,where $c$ is a constant and $k \in\{0,1,2,3,4\}$. If $\sigma^2$ is the variance of $X$ and $\mu$ is the mean of $X$,then $\sigma^2+\mu^2=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module