(5 points) John makes a measurement in a chemistry laboratory and records the re

Question

(5 points) John makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students, lab measurements is = 4 milligrams. John repeats the measurement 3 times and records the mean of his 3 measurements. What is the standard deviation of John's mean result? (That is, if John kept on making 3 measurements and averaging them, what would be the standard deviation of all his ž s?) How many times must John repeat the measurement so that the standard deviation of is at most 4?

Explanation / Answer

a)

when john keeps on averaging the averages of each 3 numbered samples, it forms a normal distribution according to central limit theorem.

std devn of the means = population stand deviation/ sqrt (n)

Therefore the standard deviation of the john's mean result is 4/sqrt(3) i.e. 2.31.

b)

Let us say john repeats it n times.

then when he wants to get it close to 4 (the population standard deviation) it may mean within 0.1 close to it. E = 0.1

And the confidence interval say is 99% then alpha is 0.01

n = z (alpha/2) * sigma ^ 2/ E = 2.57*4*4/0.1 = 412

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