00:01
Our question says that according to the national center for health statistics, in 2005, the average birth weight of newborn baby was approximately normally distributed with a mean of 119 ounce and a standard deviation of 19 ounces.
00:14
So what is the property of a new bin bobby? what's property that a newborn, a newborn baby will weigh? so we're supposed to answer the next five questions.
00:24
So our population mean meal is actually equals to 119.
00:31
Population standard division sigma is actually going to be equal to 19 so our first question says what is the probability that a new born baby will weigh more than 128 pounds so probability that x is greater than 128 so to get this value we are going to standardize the random variable i will do so by saying z is equal to x minus me divided by sigma and that has going to be 128 minus 119 divided by 19 so so using our calculator, 128 minus 1119, so that gives us 9 divided by 19.
01:08
So 9 divided by 19, that gives us 0 .47.
01:14
So that means probability that x is greater than 128 is actually close to probability that z is greater than 0 .47.
01:22
So i will be using a calculator to get this value right here.
01:26
So we have right here and this is going to be 0 .47.
01:31
And that gives us 0 .3 .1.
01:34
So the probability that a baby born today is going to have a weight of a weight more than 128 house is going to be 0 .3192.
01:45
So the second question says that less than 112.
01:49
So probability that x less than 112.
01:53
So just like we did earlier, we have a z to be cost to 112 minus 119 divided by 19 and that's minus 7 divided by 19.
02:03
So minus 7 to have by 19, that gives us minus 0 .37.
02:07
So probability that x is less than 112.
02:11
It's because the probability that z is less than minus 0 .37.
02:16
And when we do the math, so this is left stalled.
02:21
So minus 0 .37.
02:23
And there are 0 .3557.
02:26
So this is our 0 .3557.
02:30
The third question says what is a more than 144? so probability that x is greater than 144.
02:40
So we have our z to be equals to 144 minus 1119 divided by 19.
02:50
So 144 minus 119, that gives us 25 divided by 19.
02:58
So we have this to be 1 .32.
03:02
So that is probability that x is greater than 144 is equal to probability that z is greater than 1 .32.
03:11
So using our calculator, so we have right tilled and we have this to be 1 .32 and that gives us 0 .0934.
03:21
So this gives us 0 .0934...