Given
students enroll = 69%
n = 178
Find
probability that at most 67 % enrolled in college directiy after high school graduation
Explanation
Let p be the proportion of students in the united states enroll directly after high school graduation.
p = 69% = 0.69
q = 1 - p = 1 - 0.69 = 0.31
n = 178
we have to find
[tex]\begin{gathered} P(p\leq0.67)=P(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\leq\frac{0.67-0.69}{\sqrt{\frac{0.69\times0.31}{178}}}) \\ \\ P(p\leq0.67)=P(Z\leq-0.58) \\ P(p\leq0.67)=0.280 \end{gathered}[/tex]Final Answer
probability that at most 67 % enrolled in college directiy after high school graduation = 0.280