In testing a new drug, researchers found that 25% of all patients using it will have a mild side effect. A random sample of 16 patients using the drug is selected. Find the probability that more than 7 patients will have this mild side effect.

The probability that more than 7 patients will have this mild side effect is ___. (Round to three decimal places as needed.)

Answer:
Given:

Probability of success $(p)=0.25$

Sample size $(n)=16$

Solution:
The probability that more than 7 patients will have this mild side effect:
$$\text{P}(x>7)=\sum _8^{16}(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1-p{)}^{n-x}$$ $$=\sum _8^{16}(\genfrac{}{}{0ex}{}{16}{x})\cdot {0.25}^x\cdot (1-0.25{)}^{16-x}$$ $$=0.0271$$

Final Answer:
The probability that more than 7 patients will have this mild side effect $=0.0271$