Chapter 7 - The Normal Distribution With Darts Physics Lab Report PDF

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Honma 1 Michelle Honma Partner: Fara Lee Dana Rampini Physics 170 Lab February 6, 2019 The Normal Distribution with Darts Introduction: This is an experiment design to make a normal distribution by throwing darts at a paper with a target. The theory is that if a person is aiming at the bullseye then their distribution will be near or close to the bullseye with a few stragglers. Guiding Question: In Ch. 4 and 5 the idea of random errors following a normal distribution was introduced. Can an experiment be done to confirm that a measurement is distributed accordingly? Theory: The experiment is expected to make a normal bell-shaped curve when the data is plotted. If a person is aiming at the bullseye then their distribution will be similar to a normal distribution with a bell curve. Procedure: There is a paper with a bullseye and 14 bins/columns dividing the paper evenly. Each column is labeled 18 through 31 left to right. The bullseye is in the dead center of the paper between bins 24 and 25. With all participants in pairs, each pair will throw the darts at their target 100 times and record the number of times a dart lands in each bin.

Honma 2

Dartboard set up Data/Graph: Table of Data from my group’s 100 throws Bin #

18

19

20

21

22

23

24

25

26

27

28

29

30

31

# of darts

0

1

4

4

5

9

10

18

12

16

8

9

2

2

Graph 1

Honma 3 Calculations: Average bin #:

x=

∑ nx x x

N

=

∑ nxx x

100

= 25.41

nx is the number of darts in the bin, and x is the bin number. Standard deviation (sd(x)) in the bin number:

sd(x) =

√

∑ nx (x−x)2 x

N −1

=

√

∑ nx(x−x) 2 x

100−1

= 2 .64

nx is the number of darts in the bin, x is the bin number, and x is the average bin number. Standard deviation of the mean (sdm(x)) in the bin number:

sdm(x) =

sd(x) √N

=

2.64 √100

= 0.26

Confidence: 0.26 | × 1 ρ = || sdmx (x) || × 100% = || 25.41 | 00% = 1.02%

Agreement: − x class | | s = || xsdm = || 25.41−24.785 0.26 | = 2.40 (x) |

Measurement of X with its corresponding the uncertainty δX: x ± sdm ⇒ 25.41 ± 0 .26 Probability of throwing a dart in bin 23: P (23) =

9 100

= 0.09 = 9 %

Probability of throwing a dart in bin 29: P (29) =

9 100

= 0.09 = 9 %

Results: The average bin number for the darts thrown in my group is 25.41. The standard deviation in bin number for the darts thrown is 2.64. The standard deviation of the mean in bin

Honma 4 number for the darts thrown is 0.26. The confidence in results is 1.02% and the agreement of my data with the class is 2.40. For the confidence, it is within the normal parameters, 1%≤ρ≤10%. However, the agreement is not within the parameters, s...