Answer:
Given:
Probability of success $(p)=0.31$
Sample size $(n)=10$
Solution:
→ The probability that the number of college students who say they use credit cards because of the rewards program is:
(A) Exactly 2:
$P(x = 2) = \binom{n}{x} p^x (1 – p)^{n – x} = \binom{10}{2} 0.31^2 (1 – 0.31)^{10 – 2} = 0.222 $
(B) more than 2:
$P(x > 2) = \sum_{3}^{10} \binom{n}{x} p^x (1 – p)^{n – x} = \sum_{3}^{10} \binom{10}{x} 0.31^x (1 – 0.31)^{10 – x} = 0.643$
(C) Between 2 and 5 (inclusive):
$$P(2 \leq x \leq 5) = \sum_{2}^{5} \binom{n}{x} p^x (1 – p)^{n – x} $$ $$= \sum_{2}^{5} \binom{10}{x} 0.31^x (1 – 0.31)^{10 – x} $$ $$= 0.810$
