(15.10) Juan makes a measurement in a chemistry laboratory and records the resul

Question

(15.10) Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is s = 15 milligrams. Juan repeats the measurement 2 times and records the mean x of his 2 measurements.

1. What is the standard deviation (±0.01) of Juan's mean result? (That is, if Juan kept on making 2 measurements and averaging them, what would be the standard deviation of all his mean x 's?)

2. How many times must Juan repeat the measurement so that the standard deviation of mean x is 1?

Explanation / Answer

Solution:

1) Standard deviation = 15/ sqrt(n), where n is the sample size. Since the sample size is 4 in this problem, the standard deviation is 15/sqrt(2) = 15/1.4142 = 10.6067 mg.

2) 1 = 15/sqrt(n)

1 sqrt(n) = 15

sqrt(n) = 15

n = 225

Juan must repeat the measurment 225 measurements to reduce the standard deviation of x to 1

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