00:02
X is the number of kilometers traveled by airlines in thousands.
00:24
Then x is distributed normal with mean 700 and standard deviation equal to 100.
00:34
And in a we want the probability that x is between 450 and 700.
00:44
Well that is equal to the probability that 450 minus 700 divided by 100 is less than x minus mu over sigma.
01:00
And that is less than 700 minus 700 over 100.
01:08
And that is the probability that negative 2 .5 is less than standard z, less than zero.
01:19
So that is, if you look at your standard normal table, here's negative 2 .5, here's zero.
01:30
We want this probability here.
01:34
So we subtract out that half of the standard normal and subtract out that red tail.
01:44
Well this then is the probability that z is less than zero minus the probability that z is less than negative 2 .5.
01:53
And that is equal to one half minus, check my table here, 2 .5.
02:05
Let's see, 2 .5, where are you? 9, 9.
02:20
So this is minus 0 .0062.
02:31
So this is 0 .4938.
02:36
That is your answer for part a.
02:38
And then in part b, we want the proportion of planes, so the probability that 350 is less than x is less than 600.
02:54
And this all is in thousands...