I need a bit of clarification to understand sampling distributions through Khan Academy. My answer is widely different than the answers given in the sample The example question can be summarized as:
Of a population of 1750 students, 15% have reported extreme levels of stress that month. A school newspaper does not know this figure and carries out survey to determine what it is. A simple random sample of 160 students were asked if they experienced extreme levels of stress that month...10% of the sample replied "yes" to the question.
Assuming the true proportion is 15%, what is the approximate probability that more then 10% of the sample would report that they experience extreme levels of stress during the past month?
Answer: P(p>0.1)=0.96
My attempted answer is: $$\mu_{\hat{p}}=\hat{p}=0.10$$ $$\sigma_{\hat{p}}=sqrt((0.1*0.9)/160)=0.0237$$ Using these values, my cumulative probability of $P(p>10)\approx 0.50%$.
The example video uses $\mu_{\hat{p}}=p_{pop}=0.15$ but I fail to understand why because the question explicitly states that they do not know the true population parameter. Please help me clarify my understanding
