00:01
Hi, i'm david and i'm here to help you answer your question.
00:04
In this question here we are going to discuss about the central limit theorem.
00:08
Here if we have the n -quiet equal to the 30 or the population is normal already and then we will have the same amount x -pile will be approximate to the normal where we will have in such a way that the x -par will minus the mean of a standard division divide -bizabeth we obtain the standard normal.
00:32
In the question here we're given the x will be the both rate it already followed by the normal so because only follow the normal with the mean equal to the 74 standard division equal to the 12 .5 we have given the n equal to now for the part a first where we have only one single female once you find the probability that the x will be between the 68 and the 80.
01:02
Now to find this probability i convert the x into the z by using the formula for 1x.
01:07
So it means that x minus the mean over standard division, we obtain only one single z here.
01:14
Now we will have 68 and minus the mean will be the 74 of standard deviation, something on the right, and then it will compute it, we will have the z will be between 68 minus 74 divided 12 .5, equal to the minus 0 .48.
01:40
80 minus 74, divided 12 .15, equal to the 0 .48.
01:46
To find this probability, i need to bring up the z table.
01:50
Let me copy the z table and put it on the right here.
01:55
Notice that the table i bring here, it has the negative g score with the probability on the left tail.
02:00
Let me express the probability in terms of the area under the standard.
02:04
Standard normal curve.
02:06
0 here...