The probability that, among fifteen of these people, at least 10 have a college degree is ___. (Round to three decimal places as needed.)
Answer:
Given:
Probability of success $(p)=0.70$
Sample size $(n)=15$
Solution:
The probability that among fifteen of these people at least 10 have a college degree:
$$ \text{P}(x \geq 10) = \sum_{10}^{15} \binom{n}{x} \cdot p^x \cdot (1-p)^{n-x} $$ $$ = \sum_{10}^{15} \binom{15}{x} \cdot 0.70^x \cdot (1-0.70)^{15-x} $$ $$ = 0.7216$$
Final Answer:
The probability that among fifteen of these people at least 10 have a college degree $=0.7216$
