00:01
This problem says stewart's rod company manufactures stainless steel rods.
00:04
The current production process produces rods with diameters that are normally distributed with a mean of 6 .5 centimeters and a standard deviation of 0 .20 centimeters.
00:13
And we're told that they reject any rods with a diameter less than 6 .2 centimeters.
00:16
And it looks like we want to look at the second question, which says that the new process rods with diameters that are normally distributed with a mean of 6 .4 centimeters.
00:25
And we have 2 .5 % of the rods that will be produced with this new project that will be rejected because they have diameters less than 6 .2 cm, what would the new standard deviation of rod diameters be with this new production process? and to figure this out, we're looking at the probability of being less than this x value of 6 .2 being equal to 0 .025, which would be the decimal representation of 2 .5%, which means we're looking at the observation here that would have just 2 .5 or 0 .025 of the area under the normal curve less than or to the left.
01:01
And to figure out the standard deviation that would make this true, we can first find the z -score that would make this true by looking at inverse norm in our calculator, which allows us to find an observation in normal distribution with an area to the left or right of it, provided we list the area to the left first, and that's our 0 .025 with the mean and standard deviation next.
01:22
And since we're looking for the z -score currently, that would be mean of 0 and standard deviation 1...