00:01
In this problem x will be the time to perform an industrial process, and we know that variable x follows the normal distribution.
00:13
Population mean mu is 40 minutes, and population standard deviation sigma is 5 minutes.
00:23
Task a.
00:25
We should find the probability that x will be less or equal to 35 minutes.
00:32
This will be probability that z -score is less or equal to 35 minus population mean 40 divided by standard deviation 5.
00:47
And we obtain probability that z -score is less or equal to minus 1.
00:55
And now by using z -score table we can find the value of probability 0 .1587.
01:08
So this is the answer for the part a.
01:12
Next part b.
01:17
We should find the probability that x will be greater than 55 minutes.
01:24
This equals to 1 minus probability that x is less than 55 or 1 minus probability that z -score is less than 55 minus 40 divided by 5.
01:48
And we obtain 1 minus probability that z -score is less than 3.
01:57
And now by using z -score table we can find the corresponding probability 1 minus 0 .9987 and this will be 0 .0013...