5 Juan makes a measurement in a chemistry laboratory and rec

5. Juan makes a measurement in a chemistry laboratory and records the result in his lab report. Suppose that if Juan makes this measurement repeatedly, the standard deviation of his measurements will be = 6 milligrams. Juan repeats the measurement four times and records the mean x of his four measurements.

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

_________mg

(b) How many times must Juan repeat the measurement to reduce the standard deviation of x to 2?

n=________

Solution

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. Suppose that if Juan makes this measurement repeatedly, the standard deviation of his measurements will be

= 6 milligrams

repeatation of measurements (n) = 4

a) What is the standard deviation of Juan\'s mean result?

Juan\'s mean result standard deviation will be,

/ sqrt(n) = 6 / sqrt(4) = 3 milligrams

b) Given that = 6 xbar= 2 n = ?

How many times must Juan repeat the measurement to reduce the standard deviation of x to 2?

2 / 1 = 6 / sqrt(n)

sqrt(n) = 6 / 2

sqrt(n) = 6/2= 3

sqrt(n) = 3

n = (3)² = 9

n = 9