Face masks are supplied to a junior college i | vedclass

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(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

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

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(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 $10,000 	imes P(X = 0) = 10,000 	imes e^{-0.2} = \frac{10,000}{e^{0.2}}$.

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

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:

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