Math Problem Statement
A pharmaceutical company knows that five percent of all users of a certain drug experience a serious side effect. A researcher examines a sample of 210 users of the drug.
What is the probability of finding between 8 and 12 cases with side effects?
Note: Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places. What is the probability of finding more than 16 cases with side effects?
Note: Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Binomial Distribution
Probability Theory
Formulas
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
P(8 ≤ X ≤ 12) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
P(X > 16) = 1 - P(X ≤ 16)
Theorems
Binomial Theorem
Law of Total Probability
Suitable Grade Level
Undergraduate or Advanced High School (Grades 11-12)
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