SOLUTION: *** A recent clinical study, a new non-perscription anti-fungal cream showed the success rate to be 87%. If 12 people purchase the cream and use it as prescribed, what is the pro

Question 872596: ***
A recent clinical study, a new non-perscription anti-fungal cream showed the success rate to be 87%. If 12 people purchase the cream and use it as prescribed, what is the probability that at least 10 will have positive results?
Enter your response as a three digit decimal.
Answer by indra89811(24) (Show Source): You can put this solution on YOUR website!
Let p denote the event of success rate.
p=0.87
Using the Probability Binomial Distribution formula :
P(X=r)= n C r (p) ^ r (1-p )^(n-r)

The probability that at least 10 will have positive result implies that either 10, or 11 or 12 people can have positive result. i.e we are required to find P(X=10) + P(x=11) + P(x=12)
Using the above formula.
12 C 10 * (0.87)^10*(0.13)^2 + 12 C 11 (0.87)^11 * (0.13)^1 + 12 C 12 (0.87)^12 *(0.13)^0
= 0.802
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