HNC Maths Question Hand Drawn Sketch

the question is:
d) The Quality Assurance Department is anxious to improve the nominal value of the resistors to ensure more of them fall within the rated tolerance band. The manufacturing process is adjusted in an attempt to bring about this improvement. Following the adjustment, a further sample of 100 resistors is taken in order to determine if the adjustment has resulted in an improvement to the nominal value of the resistors. Analysing this second sample, it is noted that the mean value is now 21.8kΩ, with a standard deviation of 1kΩ. By comparing these new results of the resistor values following the manufacturing adjustment, with the values obtained in part (c) recorded before the adjustment, show whether or not you agree with the hypothesis that the adjustment to the manufacturing process has had a beneficial effect by making the resistor values closer to the desired manufactured nominal value of 22kΩ. Illustrate your answer with a hand drawn sketch of the normal distribution, with shaded regions representing the results of your analysis, which you can show to the Quality Assurance Manager.

i have got the answer for the 2 parts to compare but im unsure on how the graph should look and what i should be shading.

Any help from anyone?

so would this be a bell curve with my mean value as the middle and upper and lower values at each end? for example a curve going from 19 to 24 with the peak being at the mean of 21.

sorry if it sounds daft im on a distance learning course so don't actually get any classroom time just work books.

Ok. So the mean value given for this part is 21.8kohm and the values they’re looking for are between 19kohm and 24kohm. So that’s where I got the bell chart with 19 and 24 from (if this is correct) but I don’t know what I should be high lighting under the graph with the answers I have got.

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I suspect this is the original. @csutton18 to confirm.

Hopefully it's come out with sufficient resolution.

I suspect this is the original. @csutton18 to confirm.

Hopefully it's come out with sufficient resolution.

That makes a bit more sense, though the different sample sizes / standard deviations for the two samples makes a naive comparison, which I suspect they're after, a bit more approximate. For the sample in d) you (OP) have a mean estimate and you want to test whether its closer to 22, than 21.5. If youre asking about the sketch, you must have done this - what did you get? For the sketch you could illustrate 2 things
1) How the mean estimate (parts c and d) normal distributions compare to the desired mean and each other
2) How the population normal distributionns (parts c and d) meet the 22 +/-10%, so how much lies outside.
They're two different things and Id guess the question part is asking about the former (1). So as a best guess I'd sketch the normal distribution associated with the mean estimate in (d) and mark on where 21.5 and 22 lie in it, so illustrating if 21.8 is significantly closer to 22 than 21.5 which is ~the hypothesis test.

its plotting the graph im having an issue with as my work book says there is an equation of (1/(sqrt(2*pi)))*(e^(-(x^2)/2)) (in graphs software) but this is just for a standard bell curve so it doesn't help because the work book doesn't break down what each part is so i don't know where i should be inputting my answers into the equation to get a curve i need.

Its easier to say what you do understand, but a normal distribution is defined by the two parameters (mean and standard deviation). The mean represents the centre of the curve and the standard deviation determines the width. Roughly "all" (99.7% of the area) of the bell curve lies between
mean +/- 3 std dev
Similarly 95% lies between
mean +/- 2 std dev

So something like
https://www.pqsystems.com/qualityadvisor/DataAnalysisTools/capability_4.1.php#:~:text=Sketch%20a%20picture%20of%20a,curve%2C%20cutting%20it%20in%20half
or just google how to sketch a normal distribution

cheers that website was a great help. what scale do i plot on the y axis though i now know how the x axis should look but just want to make sure i have my y axis going up to the correct place or does this not really matter?

The scaling on the y-axis isnt really important and with a simple bell curve it could be omitted as youre really interested in comparing relative areas, not specific heights. However, the x-axis scaling is important (mean and std dev).

Hi sorry for the bump, I am also doing this question on my distance course (after many years of little maths)

Im not sure if i am mis-understanding the question after browsing this thread, I was going to draw two distribution graphs one for the first set with mean of 21.5 std of 2 and another for the newer set of 21.8 std of 1 and show how more of the curve is shaded on the second graph showing more resistors fall within the 19-24 area. used desmos to graph them and will have to hand draw them, am i on the right track or is it asking something else?

Hi sorry for the bump, I am also doing this question on my distance course (after many years of little maths)

Im not sure if i am mis-understanding the question after browsing this thread, I was going to draw two distribution graphs one for the first set with mean of 21.5 std of 2 and another for the newer set of 21.8 std of 1 and show how more of the curve is shaded on the second graph showing more resistors fall within the 19-24 area. used desmos to graph them and will have to hand draw them, am i on the right track or is it asking something else?

Thanks that helps a lot now just to start the laborious task of typing it all up and trying to figure out references lol