Question

Hi, can you help me answer this question please, thank you

Answer 1

EXPLANATION

We have that the mean is 95/500 = 0.19

Then, the standard error is as follows:

$SE=\sqrt[]{(\frac{0.19\cdot(1-0.19)}{500})}=0.017$

Now, the value of alpha is as follows:

$\alpha=1-\frac{95}{100}=\frac{1}{20}=0.05$

The critical probability(p*) is as follows:

$p^{}=1-\frac{\alpha}{2}=1-\frac{0.05}{2}=0.975$

Now, we need to find the z-score by assuming a normal distribution, we can use the z-score table:

z=0.8340

Next, the margin of error is as follows:

ME = 0.8340 * 0.017 = 0.0142

The confidence interval is 0.19 + or - 0.0142

0.176 < p < 0.204