00:01
First of all, let's summarize this problem.
00:03
The length of a lumber and machine cuts are normally distributed with a mean of 103 inches and a standard deviation of 0 .4 inch.
00:15
So let x will be the length of lumber.
00:35
And we know that x follows the normal distribution with population mean mu equals 103 and population standard deviation sigma equals 0 .4.
00:58
Part a, what is the probability that a randomly selected board cut by the machine has a length greater than 108 inches? so part a we should calculate probability that x greater than 103 .18.
01:30
This can be written as 1 minus p x less than 1003 .18.
01:42
And let's solve.
01:44
So this will be 1 minus p z less than 103 .18 minus 103 divided by 0 .4.
02:05
And after the calculation equals 1 minus p z less than 0 .45.
02:16
Next, using that table, we can write that this will be 1 minus 0 .6736.
02:35
And the final value 0 .3264.
02:42
So we can write the answer for the part b, that the probability that x is greater than 100...