The probability that, among eleven of these people, at least 7 prefer tea over coffee is ___. (Round to three decimal places as needed.)
Answer:
Given:
Probability of success $(p)=0.80$
Sample size $(n)=11$
Solution:
The probability that among eleven of these people at least 7 prefer tea over coffee:
$$ \text{P}(x \geq 7) = \sum_{7}^{11} \binom{n}{x} \cdot p^x \cdot (1-p)^{n-x} $$ $$ = \sum_{7}^{11} \binom{11}{x} \cdot 0.80^x \cdot (1-0.80)^{11-x} $$ $$ = 0.9496$$
Final Answer:
The probability that among eleven of these people at least 7 prefer tea over coffee $=0.9496$
