A small plant bags a blend of three types of fertilizer to meet the needs of a particular group of…

A small plant bags a blend of three types of fertilizer to meet the needs of a particular group of farmers. The different types of fertilizer are fed through three different machines. Each bag is supposed to contain 18.00 kg from machine 1, 7.00 kg from machine 2, and 5.00 kg from machine 3. It is found that the actual amounts are normally distributed about these means with the following standard deviations:

Machine	Standard Deviation
1	0.19 kg
2	0.07 kg
3	0.04 kg

a) What are the variance and coefficient of variation of the amount of fertilizer in a bag?

b) What percentage of the bags contain less than 29.50 kg?

c) How many bags must be sampled to establish with 99% confidence that the true mean is within ± 0.5% of the sample mean, regardless of what the population mean is?

 

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