00:01
The bmi of 10 year old boys is normally distributed with mean mu1 is equal to 19 .2 and standard deviation is equal to 2 .6 and let x be the random variable denoting the bmi and this x is normally distributed so mu1, sigma square which means x normally distributed 19 .2, 26 .76.
00:33
So here the proportion of a 10 year old who fall in the category underweight is given by p of x less than 14 .2.
00:45
This is equals to p of x minus mu divided by sigma less than 14 .2 minus 19 .2 divided by 2 .6.
00:56
So this is equals to p of z less than minus 1 .92.
01:02
You can also write it as 1 minus p of z less than 1 .92.
01:08
Using the standard normal table this will be 1 minus 0 .9726 which is equals to 0 .0274.
01:18
So this is the proportion of 10 year old boys who fall in the category of underweight.
01:23
Now coming to the proportion of 10 year old boys who fall in the category of healthy weight which is p of 14 .2 less than x less than 19 .4.
01:40
So this is equals to p of 14 .2 minus 19 .2 divided by 2 .6 less than x minus mu divided by sigma less than 19 .4 minus 19 .2 divided by 2 .6.
02:04
This is equals to p of minus 1 .92 less than z less than 0 .077.
02:14
So using the standard normal table we will get 0 .5306 minus 0 .0274.
02:24
So this is equals to 0 .5032.
02:30
So this is the proportion of 10 year old boys who fall in the category of healthy weight.
02:35
Now coming to the boys who fall in the category of overweight is p of 19 .4 less than x less than 22 .2...