Juan makes a measurement in a chemistry laboratory and recor

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students\' lab measurements is = 13 milligrams. Juan repeats the measurement 4 times and records the mean x¯ of his 4 measurements.

What is the standard deviation (±0.01) of Juan\'s mean result? (That is, if Juan kept on making 4 measurements and averaging them, what would be the standard deviation of all his x¯ \'s?)   

How many times must Juan repeat the measurement so that the standard deviation of x¯ is 3?       (Round your answer to the nearest whole number.)

Solution

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students\' lab measurements is = 13 milligrams. Juan repeats the measurement 4 times and records the mean x¯ of his 4 measurements.

What is the standard deviation (±0.01) of Juan\'s mean result? (That is, if Juan kept on making 4 measurements and averaging them, what would be the standard deviation of all his x¯ \'s?)   

Sd=sd/sqrt(n) = 13/sqrt(4) =6.5

How many times must Juan repeat the measurement so that the standard deviation of x¯ is 3?       (Round your answer to the nearest whole number.)

Sd=sd/sqrt(n) = 13/sqrt(n) =3

n=13²/3² =18.777

answer = 19