00:03
Now here we look at the weights of female cats, right? now according to the question, the weights of these cats are normally distributed with a mean of 4 .1 kilogram and a standard variation of 0 .6 kilogram.
00:17
And so let me denote by x the weight of a cat, and then this is the normal distribution, mean and standard deviation.
00:27
Now what proportion of female cats are weights between 3 .7 to 4 .4, right? so, and of course we can work that out, right? because you look at the probability, right? it's between this, right? now you look at this one's less than the mean, while this one's larger than mean.
00:46
So we can write actually this property as one minus alba1 minus alba 2.
00:50
And you can work at alba1 from the d score.
00:53
So the d squared alpha worm is of course given by the d square 3 .7, that's actually given 4 .1 minus 3 .7 divided by the standard deviation 3 .6.
01:03
You'll find this to be actually given by 0 .7.
01:06
So that's 0 .4 developed 0 .6, 2 over 3, right? so that's actually 0 .67, right? so you look up the d tables, and you'll find that corresponding out of a 1 is actually 25%.
01:23
Okay, so alpha 1 is about 25%.
01:26
And in a similar way, you can work out this out of a 2, right? the out of 2 is actually given by, you know, the cd score at a 4 .4, right? so you can have 4 .4 minus 4 .1 divided by 0 .6.
01:37
You'll find this to be actually half.
01:40
And then you look up the z table again.
01:42
You look at, you'll find that the corresponding out of a 2 is actually 31%.
01:48
So 31%.
01:50
So this probability, of course, is given by.
01:53
This to put together is 56, so you get this 44%.
01:57
And next one, you asked, a certain female cat has a weight that's, 0 .5 standard variations above the main, what proportion of female cats are heavier than this one...