My Math Forum Probability question

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 July 10th, 2011, 02:49 AM #1 Senior Member   Joined: Dec 2010 Posts: 233 Thanks: 0 Probability question 1.The probability that a heart patient survives after surgery in a country is 0.85. a)Find the probability that,out of five randomly chosen heart patients undergoing surgery,four survive. b)Using suitable approximation distribtuion,find the probability that more than 160 suvive after surgery in a randmo of 200 heart patient. I need help with this question. I use P(x=4) to solve part (a) but can't give the actual answer.And i am not sure what type of probability is it.I need help.Thank you.
July 10th, 2011, 04:35 AM   #2
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Re: Probability question

Quote:
 Originally Posted by hoyy1kolko 1.The probability that a heart patient survives after surgery in a country is 0.85.
Quote:
 And i am not sure what type of probability is it.I need help.Thank you.
Binomial

Quote:
 a)Find the probability that, out of five randomly chosen heart patients undergoing surgery, four survive.
$\binom{5}{4}(.85)^{4}(.15)^{1}$

Quote:
 ]b )Using suitable approximation distribution,find the probability that more than 160 survive after surgery in a random of 200 heart patient.
$np=\mu, \;\ \sqrt{np(1-p)}=\sigma$

$\mu=np=200(.85)=170, \;\ \sigma=\sqrt{200(.85)(.15)}=5.05$

Since they ask the probability of "more than 160", we use a continuity correction. Use 160.5

$z=\frac{x-\mu}{\sigma}$.

$z=\frac{160.5-170}{5.05}=-1.88$

Now, look this up in the z table.

 July 10th, 2011, 05:00 AM #3 Senior Member   Joined: Dec 2010 Posts: 233 Thanks: 0 Re: Probability question Thank you very much.I have refer to the z table i find that P Q Z 0.970 0.30 1.881 So,the probability is 0.97.Right?
 July 10th, 2011, 06:17 AM #4 Senior Member   Joined: May 2011 Posts: 501 Thanks: 6 Re: Probability question Yep.

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