SOLUTION: 1)Suppose that thepopulation variance of the amount of cooldrink supplied by avending machine is known to be 115𝑚𝑙2 i)The machine was activated 61times, and the mean

Question 1169717: 1)Suppose that thepopulation variance of the amount of cooldrink supplied by avending machine is known to be 115𝑚𝑙2
i)The machine was activated 61times, and the mean amount of cooldrink supplied on each occasion was 𝑋̅. If the upper confidence limit for a 99% confidence level is 188.20. What is the value of the sample mean 𝑋̅?
ii)What sample size is requiredif the estimateis requiredto be within 1𝑚𝑙2of the true value with probability 0.95?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
sd=sqrt(115)=10.72 ml
the half-interval for 99%CI is z*sigma/sqrt(n)=2.576*10.72/sqrt(61)=3.54
therefore the mean is 188.20-3.54 or 184.66 ml
to be within 1 ml (not sure what the 2 means there); 115 ml^2 are appropriate units for variance, but ml is appropriate for the answer.
1.96*10.72/sqrt(n)=1; sqrt (n)=21.0112, n=441.47 or 442
sample size is 442.
RELATED QUESTIONS
1. Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is... (answered by Boreal)

suppose a brewery has a filling machine that fills 12 ounce bottles of beer. it is known... (answered by Theo)

A manufacturer of salad dressings uses machines to dispense liquid ingredients into... (answered by CPhill)

The school of Science and Engineering at a local university regularly purchases a... (answered by ewatrrr)

A machine that stuffs a cheese filled snack product can be adjusted for the amount of... (answered by Theo)

A machine has an efficiency of 91%. If the energy supplied to the machine is 4,000 watts, (answered by Alan3354)

A vending machine distributor wants to be 98% confident that the coffee machine is... (answered by stanbon)

a machine fills one-pound cartons of Top Flavor ice cream. The machine can be set to... (answered by ewatrrr)

A manufacturer of salad dressings uses machines to dispense liquid ingredients into... (answered by ikleyn)