A high-speed packing machine can be set to deliver between 11 and 13 ounces of a

Question

A high-speed packing machine can be set to deliver between 11 and 13 ounces of a liquid. For any delivery setting in this range the amount delivered is normally distributed with mean some amount and with standard deviation 0.08 ounce. To calibrate the machine it is set to deliver a particular amount, many containers are filled, and 25 containers are randomly selected and the amount they contain is measured. Find the probability that the sample mean will be within 0.05 ounce of the actual mean amount being delivered to all containers.

Explanation / Answer

for z score =(X-mean)/std deviation

for std error of mean =std deviation/(n)1/2 =0.08/(25)1/2 =0.016

hence

probability that the sample mean will be within 0.05 ounce of the actual mean amount being delivered to all containers =P(-0.05/0.016<Z<0.05/0.016)= P(-3.125<Z<3.125)=0.9991-0.0009 =0.9982

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