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Use da table 2 answer da question

Da table represents da frequency of ccurences 4 numbers 2, 4, 6, 8, and 10 when jade tossed a cube.

Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8

Jede tossed a cube with faces number with 2, 4 6, 8, 10 and 12 da results r recorded in da table wut is da smallest discrepancy between da experimental n da expect pribakuty uwth dsi experiment? Write ur asner in 3 decimal places rounded 2 da nearest thousandth

1 answer

To find the smallest discrepancy between the experimental frequencies and the expected probabilities based on the outcomes, we first need to determine the expected frequencies.

The outcomes and their experimental frequencies are:

  • Outcomes: 2, 4, 6, 8, 10, 12
  • Frequencies: 10, 9, 6, 15, 13, 8

Total number of tosses = 10 + 9 + 6 + 15 + 13 + 8 = 61

Next, we will calculate the expected frequency for each outcome assuming each outcome has an equal probability, which can be calculated as:

\[ \text{Probability for each outcome} = \frac{1}{6} \]

Then, the expected frequency for each outcome is calculated as:

\[ \text{Expected frequency} = \text{Total tosses} \times \text{Probability for each outcome} = 61 \times \frac{1}{6} \approx 10.167 \]

Now, we need to calculate the discrepancy for each outcome, which is the absolute difference between the experimental frequency and the expected frequency:

  1. For outcome 2:

    • Experimental: 10
    • Expected: 10.167
    • Discrepancy: |10 - 10.167| = 0.167

  2. For outcome 4:

    • Experimental: 9
    • Expected: 10.167
    • Discrepancy: |9 - 10.167| = 1.167

  3. For outcome 6:

    • Experimental: 6
    • Expected: 10.167
    • Discrepancy: |6 - 10.167| = 4.167

  4. For outcome 8:

    • Experimental: 15
    • Expected: 10.167
    • Discrepancy: |15 - 10.167| = 4.833

  5. For outcome 10:

    • Experimental: 13
    • Expected: 10.167
    • Discrepancy: |13 - 10.167| = 2.833

  6. For outcome 12:

    • Experimental: 8
    • Expected: 10.167
    • Discrepancy: |8 - 10.167| = 2.167

Now, we will summarize the discrepancies:

  • Discrepancy for 2: 0.167
  • Discrepancy for 4: 1.167
  • Discrepancy for 6: 4.167
  • Discrepancy for 8: 4.833
  • Discrepancy for 10: 2.833
  • Discrepancy for 12: 2.167

The smallest discrepancy is 0.167, which we can round to three decimal places:

Answer: 0.167