Question

QUESTION 7 1 poit Exhibit 7-3 In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study Refer to Exhibit 7-3. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is O 0.4664 O 0.9328 0.9664 0.0336

Answer 1

Since , the sampling distribution of the sample porportion is ,

$\hat{p}\to N(\mu_{\hat{p}}=p,\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}})$

Now ,

$P(P\geq 0.30)=P(\frac{P-\mu_{\hat{p}}}{\sigma_{\hat{p}}}\geq \frac{0.30-0.40}{\sqrt{\frac{0.40(1-0.40)}{80}}})=P(Z\geq -1.83)$

$=1-P(Z< -1.83)=1-\Phi(-1.83)=1-[1-\Phi(1.83)]=\Phi(1.83)$

$=0.9664$ ; From standard normal distribution table