Question

According to data released in 2016, 69% of students in the United States enroll in college directly after high school graduation. Suppose a sample of 178 recent high school graduates israndomly selected. After ventying the conditons for the Central Limit Theorem are met. find the probability that at most 67 % enrolled in college directiy after high school graduaton

Answer 1

Given

students enroll = 69%

n = 178

Find

probability that at most 67 % enrolled in college directiy after high school graduation

Step-by-step 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

`\begin{gathered} P(p\leq0.67)=P(\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\leq\frac{0.67-0.69}{\sqrt{(0.69*0.31)/(178)}}) \\ \\ P(p\leq0.67)=P(Z\leq-0.58) \\ P(p\leq0.67)=0.280 \end{gathered}`

Final Answer

probability that at most 67 % enrolled in college directiy after high school graduation = 0.280