The theoretical probability of each section is 1/8, since there are 8 equal-sized sections on the spinner. To find the theoretical frequency, we multiply the theoretical probability by the total number of spins:
Theoretical frequency = (1/8) x 450 = 56.25
We can then calculate the experimental probability for each section by dividing the frequency by the total number of spins:
Experimental probability = Frequency/Total number of spins
Using this formula, we can calculate the experimental probabilities for each section:
Part 1: Experimental probability = 58/450 ≈ 0.129
Part 2: Experimental probability = 52/450 ≈ 0.116
Part 3: Experimental probability = 39/450 ≈ 0.087
Part 4: Experimental probability = 77/450 ≈ 0.171
Part 5: Experimental probability = 50/450 ≈ 0.111
Part 6: Experimental probability = 43/450 ≈ 0.096
Part 7: Experimental probability = 60/450 ≈ 0.133
Part 8: Experimental probability = 71/450 ≈ 0.158
To find the number with the greatest difference between the theoretical and experimental probability, we can calculate the difference between the two probabilities for each section:
Part 1: |0.125 - 0.129| = 0.004
Part 2: |0.125 - 0.116| = 0.009
Part 3: |0.125 - 0.087| = 0.038
Part 4: |0.125 - 0.171| = 0.046
Part 5: |0.125 - 0.111| = 0.014
Part 6: |0.125 - 0.096| = 0.029
Part 7: |0.125 - 0.133| = 0.008
Part 8: |0.125 - 0.158| = 0.033
As we can see, the greatest difference between the theoretical and experimental probability is for Part 4 with a difference of 0.046. This indicates that the experimental frequency for Part 4 is significantly different from the theoretical frequency, which may suggest that the spinner is biased towards that section.