- #1
Perrault
- 14
- 0
Homework Statement
(I translated this from french)
Some n dice are thrown and the sum of all their face values is 117.
Estimate n through a confidence interval of 90%.
In other words, of all the possible rolls of n dice that sum up to 117, find a range in which n should be located 90% of the time.
For example, 20[itex]\leq[/itex]n[itex]\leq[/itex]117, 100% of the time because a 117-dice roll can sum up to 117, but not a 118-dice roll, and 19 dice can give a maximum sum of 114.
Homework Equations
To estimate the population average (here, the population is every possible roll of n dice that sums to 117) while the variance is unknown, and X is normally distributed (which it probably is), we use the following formula
[itex]\frac{X^{―} - \mu}{\sqrt{\frac{S^{2}_{n-1}}{n}}
}[/itex] : T[itex]_{n-1}[/itex]
Where :
X[itex]^{―}[/itex] is the sample average if that has anything to do with anything.
S^{2} _{n-1} would be equal to [itex]\frac{n}{n-1}[/itex] S[itex]^{2}[/itex] where S[itex]^{2}[/itex] would be the sample's variance and n the number of items in the sample.
T[itex]_{n-1}[/itex] is the symbol for Student's t-distribution.
There are five other, closely related, formulae, but this is the one that seems the most reasonable to use.
But I'm not even sure how that can be used to estimate n.
The Attempt at a Solution
What has been shown above probably shows at which point I am lost in this affair. We have to use some distribution, but I'm not even sure my choice is right.
Thanks!