00:01
Hello, students, we need to write here weight of female cats of and certain breed are normally distributed, meaning standard aviation is given.
00:09
So in the first case, we need to find what proportion of female cats have a weight between these values and how heavy is a female cat whose weight is on 18 percentile.
00:18
So what we are given right here, we are given normal distribution if i draw for it.
00:24
According to normal distribution, if i write here, that says this is our a part and this is our b part to make it more.
00:31
More clear so here we need to add here normal distribution is the distribution in which all the random variables are distributed amongst well -shaped curve this is z minus z this is probability of pz sum of all probabilities is equal to one and total area under normal distribution curve is basically equals to one right -hand side areas point five left -hand side area is point five it means that area is symmetric about y -axis we need to write here so basically if i write here for this, what would be our z score value which is z1 is equal to x minus mu divided by sigma.
01:10
So x is basically equals to we need to write here.
01:14
This is mean, so 3 .7 minus 3 .7 minus 4 .1 divided by sigma.
01:21
So sigma value is basically 0 .6, we need to write here.
01:25
And z2 value is basically we need to write here.
01:29
This is 4 .4 minus 4 .4 minus 4 .1 let's erase this this is 4 .4 minus 4 .1 divided by 0 .6.
01:41
So finally we can write here if i write here for this.
01:44
So this will come out as minus 0 .67 and this is 0 .5.
01:49
So finally we can write here we need to calculate our.
01:53
So in the first case what we need we need proportions.
01:56
So for there we need our probability value...