SOLUTION: The recovery rate of cattle from a certain disease is 0.22. If 200 cattle are affected what is the probability that at least 51 will recover?

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Question 383496: The recovery rate of cattle from a certain disease is 0.22. If 200 cattle are affected what is the probability that at least 51 will recover?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Use the normal approximation to the binomial distribution:
n = 200, p = 0.22, q = 0.78, mu+=+np+=+44, and sigma+=+sqrt%28npq%29+=+sqrt%28200%2A0.22%2A0.78%29+=+5.85833. Then P%28X+%3E=+50.5%29+=+P%28%28X+-+mu%29%2Fsigma+%3E=+%2850.5+-+44%29%2F5.85833+=+1.1%29. Thus P%28X+%3E=+50.5%29+=+P%28Z+%3E=+1.1%29+=+0.1357.