Normal Distribution problem

Mar 2010
3
0
A factory has a machine designed to produce 1 kg bags of sugar. It is found that the average weight of sugar in the bags is 1.02 kg. Assuming that the weights of the bags are normally distributed, find the standard deviation if 1.7% of the bags weigh below 1 kg.
Give your answer correct to the nearest 0.1 gram.
I know how to find the percentage by using mean and standard deviation, but I do not understand how to get standard deviation from just the mean and percentage. Please help, it would be greatly appreciated.
 

pickslides

MHF Helper
Sep 2008
5,237
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Melbourne
, but I do not understand how to get standard deviation from just the mean and percentage. Please help, it would be greatly appreciated.
Let's say \(\displaystyle P(z<a)=0.017\)

By the normal distribution table \(\displaystyle P(z<-2.1201)=0.017\)

And

\(\displaystyle -2.1201=\frac{X-\mu}{\sigma}\)

Can you finish it off?
 
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