SHOW ALL WORK 1 An experimental measurement has a result 4

SHOW ALL WORK !!!!!!!!!!!!!

1.

An experimental measurement has a result ( 4.5 ± 0.3)m , and a predicted value of 5.2m. How many standard deviations is the experimental measurement from the predicted value? What is the percent age uncertainty? What is the percent difference between the experimental value and the predicted value?

PART A : Look at the results of calculations made in #1, what can be said of the measurement in

terms of the predicted value? Explain.

PART B: Looking again at the results in #1, would you say the experiment used a precise method of

measurement? Explain

Solution

measured value = 4.5 m

standard deviation /uncertainty = 0.3

one sigma spread = 4.8 – 4.2

two sigma spread = 5.1 – 3.9

three sigma spread = 5.4 – 3.6

The predicted value 5.2 is 3- standard deviations from the measure value.

Percent uncertainty = 0.3/4.5*100 = 6.67 %

Difference form predicted value = 5.2 – 4.5 = 0.7

Percent difference = (0.7/4.5)*100 = 15.56 %

PART A: the experimental values are in agreement with the predicted values as they are in ±3 population, which covers 99% 0f the distribution.

PARTB: Not very precise as the percentage uncertainty 6.67 % a little on the higher side.