# where 30%of all admitted patients fail to pay their bills and the debts are eventually forgiven suppose that the clinic treats 2000 different patients

where 30% of all admitted patients fail to pay their bills and the debts are eventually forgiven. suppose that the clinic treats 2000 different patients over a period of 1 year, and let x be the number of forgiven debts. a. what is the mean (expected) number of debts that have to be forgiven? b. find the variance and standard deviation of x. c. what can you say about the probability that x will exceed 700?
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From the given information we have 30% of patients fail to pay medical bills and the debts are eventually forgiven. Number of patients treated is 2000. Here Probability of successes $p=0.30,$ Probability of failure $q=0.70,$ and $n=2000$ Let x be the number of forgiven debts a) We find the mean number of debts that have to be forgiven. According to binomial distribution the mean $\mu =np$ $\mu =np$
$=2000\left(0.3\right)$
$=600$
b) According to binomial distribution variance ${\sigma }^{2}=npq$ ${\sigma }^{2}=npq$
$=2000\left(0.3\right)\left(1-0.3\right)$
$=420$
Standard deviation is $\sigma =\sqrt{}$ npq $\sigma =\sqrt{n}pq$
$=\sqrt{420}$
$=20.4939$
c) Mean $\mu =600$ Standard deviation $\sigma =20.4939$ According to Tchebysheff's Theorem almost all the debts will lie within three standard deviations of the mean, $\mu ±3\sigma =\left(600-3\left(20.4939\right),600+3\left(20.4939\right)\right)$
$=\left(538.5183,661.4817\right)$
Therefore, the probability that the number of forgiven debts will exceed 700 would be zero. Because it exceeds the value 661.48