4 3/9 points | Previcus Answers BaldiStat3 13.E.C06. My Note uan makes a measure

Question

4 3/9 points | Previcus Answers BaldiStat3 13.E.C06. My Note uan makes a measurement in a chemistry aboratory and records the result n measurement 3 times and records the mean x of his 3 measurements. s lab report. The standard deviation ofla measurements made by students is . 35 m g arms. uan repeats e (a) What is the standard deviation of Juan's mean result (That is, if Juan kept on making 3 measurements and averaging them, what would be the standard deviation of all his x's? Round your answer to 3 decimal places.) x milligrams (b) How many times must Juan repeat the measurement to reduce the standard deviation of x to 7? X times Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement. The average of several measurements is more likely than a single measurement to be close to the mean The result of a single measurement will never be close to the mean The average of several measurements will always be an unbiased estimate of the mean. Taking several measurements reduces the likelihood of reporting error.

Explanation / Answer

Solution:-
a) The standard deviation of juan's mean : 35/sqrt(3) = 20.207

b) Assume he has to repeat the meaurement n times to reduce it to 5.
=> 35 /sqrt(n) = 7

We want to solve for n
  
=> 35 = 7*sqrt(n)

5 = sqrt(n)

Square both sides

25 = n

  
he has to measure 25 times to reduce the standard deviation of Xbar to 7

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