Pregunta
- 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
- 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]
recorded. Find the mean and standard deviation of
and
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
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%
Solución

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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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