0:00
All right.
00:01
So here the question says that the chickens of ornix farm are processed when they are 20 weeks old.
00:07
So the distribution of their weights is normal with the mean of 3 .8 lb and standard deviation of 0 .6 lbs.
00:16
Then the farm has created three categories for these chicken according to their weight.
00:21
So petite means that their weight is it is less than sorry this is.
00:34
Is less than 3 .5 lb right then the standard category that is the ways between 3 .5 and 4 .9 lb and big when the weight is above 4 .9 lb.
00:53
Now first part of question here is what proportion of these chickens will be in each category? alright so here okay so petite means that the probability here that the weight is less than 3 .5 right so this will be x minus mean upon standard deviation less than 3 .5 minus 3 .8 divided by 0 .6 so this is equal to probability of z less than minus 0 .5 right so this will be equal to this is 0 .385 right next category is the category that is big one.
01:42
So for this we need to compute the probability that the weight is more than 4 .9, right? so again, we are going to use the same formula here.
01:50
That is x minus mean upon standard deviation greater than 4 .9 minus 3 .8 divided by 0 .6.
01:59
So this is equal to probability of z greater than 11 upon 16.
02:06
And this we can obtain from the z table.
02:09
This is 0 .0334.
02:13
Right now in the standard category is the one.
02:18
For the standard we need to compute that the probability is between 3 .5 less than 4 .9 or this we can write it as that the probability of z less than 4 .9 minus probability of z less than 3 .5.
02:38
Now this will be equal.
02:42
To 1 minus probability of z greater than 4 .9 minus probability of z less than 3 .5 right now these probabilities we have already determined so this is 1 minus 0 .3085 minus 0 .0334 so that will be equal to 0 .6581 right and in the next part of the question is to determine the 60th percentile of the distribution of the weight, right? thus, that the probability of x is less than c is equal to 0 .60.
03:27
So we have to compute the value of c here...