00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
Now let me bring up your question here.
00:06
In the question here, we'll you discuss about the sampling distribution on the sample proportion let me remind you that if we have the n is large and then the sample proportion p heart will be approximate to the normal with the mean equal to the p, standard division pht equal to the square root of the p times 1 minus p divided by n.
00:28
And because it follows by the normal, it will turn the p hath minus mule on the standard division, we obtain the standard normal.
00:37
In this question here, we given the p equal to the 0 .26, and it will equal to the 72, and therefore the p hath will be approximately to the normal, with the mean, it will equal to p, 0 .26, and the standard division equal to the square root of the 0 .26 times 1 minus 0 .206.
00:59
Divided by n 72 and then we get equal to 0 .26 times 0 .74, divided by 72, taking the square root, equal to the 0 .0517.
01:17
And this will be the answer for the first part here about the distribution of the phearts.
01:22
Now for the b, once you find the probability that the p heart, it will be more than 0 .110.
01:29
To find this probability, i need to apply the formula here to convert the b heart into the z.
01:36
And to do it, i will change the 0 .18 and minus the mean will be 0 .26 over the standard deviation.
01:46
Then we get equal to the probability smaller than 0 .18 minus 0 .26 divided by the standard deviation minus 1 .5 .5.
01:58
To find this probability, i need to bring up the zs more than the zon8.
02:01
So let me copy the z table and i put it on the right here.
02:08
Now the table i bring here it has the negative g score with the probability on the left tail.
02:13
So it's compatible with this probability with the g score equal to minus 1 .5 and 5...