SOLUTION: An African hospital is treating patients who have Lhassa Fever. Seventy percent of patients with this disease die, and each patient lives or dies independently of other patients.

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Question 44280: An African hospital is treating patients who have Lhassa Fever. Seventy percent of patients with this disease die, and each patient lives or dies independently of other patients.
Suppose over along period, the hosptial expects to treat 100 patients. What is the mean number of deaths expected during this period? My answer is 100 x .70 = 70 patients.
The 2nd part of that is suppose over a long period, the hospital expects to treat 100 patients. What is the standard deviation of the number of deaths expected during this period? (I am not sure how to begin finding this answer)
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
You calculated the mean number of deaths correctly.
Regarding the standard deviation, notice that the number of deaths follows a binomial distribution, with parameters n = 100 (the total number of patients) and p = 0.7 (the probability of a "success", in this case, that the patient dies, which is 70%). The variance of variable that follows a binomial distribution is given by:
n%2Ap%2A%281-p%29
Pluging the appropiate parameters,
100%2A0.7%2A%281-0.7%29+=+21
Finally, since the standard deviation is the square root of the variance, the we get that the std dev of the number of deaths is:
sqrt%2821%29+=+4.5825

I hope this helps!
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