I was currently solving one of the past papers from CAIE 9709/72/M18 and this is regarding Q7 of that paper. The question is as follow:
A nutritionist wishes to investigate the mean sugar content in some cereal bars. He takes a random sample of 10 of the bars and measures the mass, in grams, of sugar in each bar. His results are shown below.
11.9 11.7 11.8 11.9 11.6 12.1 11.7 11.9 11.8 11.9
Assume that the mass, in grams, of sugar in bars of this type has the distribution N(μ, 0.01)
a) Calculate 99% confidence interval for μ
The problem arises that I'm taking standard deviation as 0.01 however in the marking scheme they have taken 0.1. I'm wondering where this 0.1 is coming from? Shouldn't it be 0.01? The sample mean being 11.83 and the standard deviation side being 0.01/√10. Since it is a 99% confidence interval so z is 2.576. While all my other values are the same as the marking scheme, only my standard deviation value is different which ultimately makes my final answer mismatched with the marking scheme. I would really appreciate it if someone could tell me whether I'm making a mistake or is this an error on their behalf.
I'm attaching below the link of the marking scheme of the past paper as well: https://papers.gceguide.com/A%20Levels/Mathematics%20(9709)/2018/9709_m18_ms_72.pdf