SOLUTION: Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of

Question 241382: Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect? Round answer to 4 decimal places.
I think I know how to compute for "exactly three students," but I cannot figure out how to do "more than three students"
Here's how I approached "exactly three":
p = 0.03, q = 1 - p = 0.97, n = 150
P(r, n) = nCr (p)^r * (q)^(n - r)
P(3, 150) = 150C3 * 0.03^3 * 0.97^147 = 0.1691
Since I am trying to figure out how to do these types of problems on my own, please include the steps.
Thank you!

Found 2 solutions by edjones, stanbon:
Answer by edjones(7311) (Show Source):
You can put this solution on YOUR website!
You are correct so far as you have gone.
Now do the same procedure for exactly 2, 1 and 0 students.
Find the sum of the 4 probabilities and subtract it from 1 and you have your answer.
.
Ed

Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!
Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect? Round answer to 4 decimal places.
I think I know how to compute for "exactly three students," but I cannot figure out how to do "more than three students"
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You should have or you need a cumulative binomial chart or a calculators
with a Stat function.
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Your problem:
Binomial with n = 150, p = 0.03, 4 <= x <= 150
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Your problem:
P(4 <= x <= 150) = 1 - P(0 <= x <= 3)
= 1 - [P(x= 0) + P(x=1) + P(x=2) + P(x=3)]
= 1 - [0.01037 + 0.048106..+ 0.110843 + 0.16912...)
= 1 - [0.33844
= 0.66156...
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Stan H.