Pregunta
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  1. A fair six-sided die is thrown 20 times and the number of sixes, , fair six-sided die is thrown 20 times and the number of odd-numbered scores, , is
    recorded. Find the mean and standard deviation of . [5]
    and respectively, where and , . Find the probability that
  2. The masses, in grams, of large bags of sugar and small bags of sugar are denoted by
    the mass of a randomly chosen large bag is less than twice the mass of a randomly
    chosen small bag. [5]

Ask by Pena Bolton. in the Philippines
Jan 22,2025

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Problem 1:
  • Mean of : or approximately 13.33
  • Standard Deviation of : or approximately 2.11
Problem 2:
  • Probability that a large bag is less than twice the mass of a small bag: 37.5%

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Extra Insights

If you’re rolling a fair six-sided die, you have a probability of for rolling a six, and since you’re throwing it 20 times, the expected number of sixes would be . For odd-numbered outcomes, you can get 1, 3, or 5, making it a total of 3 odd outcomes out of 6. Hence, the average number of odd scores in 20 throws is .
To find the mean and standard deviation of , you add the means: . The variances sum up too, so gives you the total variance. If and , calculate the variances and , yielding . Therefore, you’d have .
Regarding the comparison of mass between the large bags and small bags of sugar, you’re trying to find . This involves combining the distributions with the method of transformation. Calculate which has the mean and double the variance. Generally, you can standardize it using the z-scores to find this probability, and it might yield a bit of mathematical exploration along the way!

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