1) You measure a velocity of some particles many thousands of times, and find th

Question

1) You measure a velocity of some particles many thousands of times, and find that the average is 90.7 m/s, and that the standard deviation on an individual measurement is 2 m/s. Now, you take an additional 20 measurements, and take the average just of those 20 measurements. What is the probability that you find that average to be either greater than 91.6 m/s, or less than 89.8 m/s?

3) We have a function z = xcos2(?). We are interested in how sensitive the function is to the uncertainty ?? for different values of ?.

a. Take x = 1.203 +/- 0.002 meters, ? = (45.5 +/- 0.5) degrees. Calculate z

Explanation / Answer

1)

P(x>91.6) + P(x<89.9) = P(z> (91.6-90.7)/2) + P(z<(89.9-90.7)/2)=0.3264 + 0.3446 =0.671

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