00:01
Hey there, welcome to numerade.
00:03
So we are looking here at the range of the gestational age.
00:08
We're given the mean of the weight of these newborn babies here, and the standard deviation.
00:17
So we have to find the following probabilities.
00:20
Let's write down our mean and standard deviation first.
00:23
We're given a mean of 3 ,580.
00:31
We're given a standard deviation.
00:35
Of around 620.
00:39
So with this here, we're trying to find the probability of a randomly selected baby is between these two ways, 3 ,520 and 4 ,000.
00:53
So where x is between 3 ,520 and 4 ,000.
01:03
All right.
01:10
So in order to find its probability, we had to split the probability into two parts.
01:17
X is less than 4 ,000.
01:18
4 ,000 and the probability the x is less than 3 ,520.
01:30
So let's do x is less than 4 ,000 first.
01:33
We're going to set up a z square equation.
01:36
So we take our value 4 ,000, subtracted to our mean, which is 3 ,580, divided by our standard deviation, 620.
01:54
This gives us a z score of around.
01:57
Let's see here, 0 .68.
02:02
Now we can use the z score to find our probability by utilizing a table or a calculator.
02:09
The probability that we get is 0 .75 .9.
02:14
So let's save this probability here for a later.
02:23
Okay, so let's do the next one.
02:26
$3 ,520, minus our mean of $3 ,580, divided by our standard deviation of 620.
02:41
This gives us a x a z score of 3 ,520 minus 3 ,580 divided by 620, we get around negative 0 .1, which gives us a probability of 0 .4615.
03:06
So now to find our answer here in between, we're going to take our larger probability, subtracted to the smaller probability that we found.
03:23
Let's see what we get.
03:32
Okay, we get overall probability of 0 .2895.
03:42
All right.
03:45
Perfect.
03:46
So that's our probability for part a.
03:49
Let's move on to part b...