please answer all questions Question3 Machine A, used for filling bags with grou

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please answer all questions

Question3 Machine A, used for filling bags with ground coffee, can be set to dispense any required mean weight of coffee per bag. At any setting the weight of coffee in a bag can be modelled by a normal distribution with a standard deviation of 1.95g (a)If the machine is set to dispense a mean weight of 128g of coffee per bag, calculate the percentage of bags that contain less than 125g To meet an official regulation the setting on a machine must be adjusted so that no more than 1% of bags contain less than 125 (b) ()Calculate the smallest mean weight to which machine A should be set to meet the regulation. (") Machine B will only just meet the regulation when it is set to dispense a mean weight of 128.5g. Assuming that the weight of coffee is a bag filled by Machine B can be modelled by a normal distribution, calculate the standard deviation of this distribution

Explanation / Answer

a)

b)

here for 1 percentile z score =-2.3263

therefore required mean weight =X-z*std deviation =125-(-2.3263)*1.95 =129.54

ii)

std deviation =(X-mean)/z score =(125-128.5)/(-2.3263)=1.5045~ 1.50

for normal distribution z score =(X-)/ here mean=       = 128 std deviation   == 1.950

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