Please help me solve this Juan makes a measurement in a chem

Please help me solve this.

Juan makes a measurement in a chemistry lab and records the result in his lab report. The standard deviation of students lab measurements is s.d=10 milligrams. Juan repeats the measurements 3 times and records the mean xbar of his 3 measurements.

How many times must Juan repeat the measurement to reduce the standard deviation of x bar below 3?

Solution

Assume he has to repeat the meaurement n times to reduce it to 3.
10 /sqrt(n) = 3
We want to solve for n
10 = 3 sqrt(n)
3.333 = sqrt(n)
square both sides
11.111 = n
He has to measure 11.11 times to reduce the standard deviation of xbar below 3 .