Standard Deviation percentage increase

Dear John,
Firstly thanks a lot for providing us with all these resources. Very appreciated.

I am having issues understanding the tail end probability. I have looked at Ask the Tutor to see if this question was asked before but couldn’t find it. Apologies if it was.

ex: normal distributed with a mean of 8kg and st.dev of 0.02kg

(a) if items whose weight lies outside the range 7.985 – 8.035kg are deemed to be faulty, what % of products would be faulty.

* i have no problem with this part of the question, it is 26.67%.
I thought i should write section (a) too to give you the full scenario.

My issue is with b and c (if b is found then c would make sense too)

(b) if it is required to reduce the % of items that are too heavy (with a weight over 8.035kg) to 2%, to what value must the mean be decreased, leaving all other factors unchanged.

(c) if required to reduce the % of items that are too light (with weight below 7.985kg) to 2%, to what value must the standard deviation be decreased, leaving all factors unchanged.

answer (b): The tail end probability of 2% corresponds to the table entry 48%, so the z value 2.05 so work back to calculate the mean 8.035-(2.05*0.02) = 7.994

What does not make sense to me is that isn’t the percentage of items which are heavier than 8.035kg is 4.01% with the current mean of 8kg? (0.5-0.4599)= 0.0401

isn’t this 4.01% the one that what we are trying to reduce to 2%?

I can’t get my head around the answer “the tail end probability of 2% corresponds to the table entry 48% so the z value is 2.05”

why is it 48%? is it because 50% – 2%=48%

Apologies if i am being silly here. I have watched your free lectures and they all made sense and I like the way you are “explaining” the formulas so they make “sense” to us. This is exactly what I really need here. I just couldn’t understand this answer; it just didnt make sense to me. Would you mind helping me understand it?

Thanks in advance
Regards
Mia