0:00
Hello.
00:03
So for the first part, x is going to be not only distributed the mean standard division, sample standard division.
00:19
So we have an average of 145.
00:26
So we can rewrite this as 145.
00:31
So the sample standard division is going to be equal to the standard division over the square root of the sample size.
00:39
So we have a standard division 14 and the square root of the sample size is going to be 49 square root of 49 is 7 14 7 is 2 it won't be 2 the second part of the question is looking for a probability some average between 142 and 146 so that's going to be equal to a probability so here you want x minus mu over standard degrees of square root of n.
01:36
So this side, on the left, we're going to have one for two minus the minute's 145 over.
01:51
But you know that this one here is that, right? that's 14 over square root of 49, so that's just 2.
02:03
So this is also going to be 146 minus 145 over 2 so that is going to be negative that's going to be negative 3 over 2 that's negative 1 .5 so less than z less than this is going to be what 1 over 2 that 0 .5 alright so we can rewrite this as the probability of z less than 0 .4 minus the probability of z less negative 1 .5.
02:50
So at this point, we're going to need the z table to figure this out.
02:53
So from the z table, we look for the probability when z is 0 .5.
03:00
So when z is 0 .5, the probability is 0 .6 -9146.
03:11
Let's 0 .6, 9146.
03:15
And then 1 z is negative 1 .5.
03:22
Let's see.
03:24
That is 0 .0681.
03:31
0 .06681.
03:35
So the difference is going to give us our probability.
03:38
So 0 .69146 minus 0 .066.
03:47
686...