00:01
All right, so for a, we want to find the probability of a pregnancy lasting less than 143 days.
00:11
So using a z -score approach, it's gonna be 143 minus 147 over 12.
00:23
That's gonna give us negative .33.
00:28
So using a z -table or a z -calculator, let's find that probability.
00:37
And that's gonna give us 0 .3707.
00:43
For b, oh, i guess we have, so if 100 pregnant individuals are selected independently from this population, we would expect 37 % of pregnancies to last less than 143 days.
01:11
So if we want to, 37 % would be less than 143 days, but then 60, yeah, 63 % would last more than 143 days.
01:32
So now for b, for a random sample of 19 pregnancies, describe the sampling distribution for the sample mean.
01:39
So the sample mean, we'll follow a normal distribution with 147 as our mean, and then we'll have 12 divided by the square root of 19 for our standard error.
01:53
So this would be normal.
01:57
So for c, there's probability of the mean being less than 143 and probability of x bar being less than 143.
02:08
So similar approach.
02:11
Now we're gonna have 143 minus 147 over 12 divided by the square root of 19.
02:21
And that's gonna give us negative 1 .452.
02:29
So let's toss that in, find our probability.
02:31
And that gives us 0 .0732...