00:01
Hey there, welcome to numerate.
00:02
So we are given the lengths of lumber that a machine cuts into.
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We're given the mean of 102 inches and a standard deviation of 0 .3 inches.
00:13
So with this, what is the probability that the board that is cut by the machine is greater than 102 .07 inches? so this will be set up with a z score equation.
00:27
So we will have z equals.
00:31
So we're going to be given the x value, which is 102 .07, minus the noted mean, which is 102, divided by.
00:50
So this is going to be divided by, let's see, the standard deviation, which is 0 .3 inches.
00:58
And we're going to calculate the z score here.
01:02
Calculate below.
01:06
Okay.
01:07
And we would get a z score of around 0 .233.
01:13
But let me see about rounding.
01:15
It says round to four decimal places.
01:17
So 0 .2 -333.
01:25
So this would be z score.
01:27
So it would just be 0 .23.
01:31
So with that, we can find a probability.
01:34
So what we're looking for is a probability that x would be greater than our value over here.
01:41
So we're given a z course, so let's write z is, let's see, greater than 102 .07, so it'll be 0 .23 equals...