13. In the lab, a group carefully measures the weight of the same item four times with the following results. Answer the following questions to show how the answer should be reported to account for precision. Trial Mass 1 12.3569 g Standard deviation equation 12.3572 g (x, - ) n- 1 3 12.3583 g 12.3566 g Calculate the average mass (x). a. b. Complete the following table to find E(x,-x)*. Trial Mass (x) (x,-x)² (mass-average mass)? 1 12.3569 g 12.3572 g 12.3583 g 3 4. 12.3566 g c. Calculate the standard deviation of the measurement using the equation shown above. d. Report the measurement in the format average mass (±) standard deviation. 33 Review of Mathematics
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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