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# S2 approximation help

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1. A far die is rolled and the number of sixes is obtained and recorded. Using suitable approximations, find the probability of at least 25 sixes in 120 rolls of the die.

Cant use poisson as Mean is 20 as p=1/6 and n=120
Cant use normal as p isnt close to 0.5
2. (Original post by fpmaniac)
A far die is rolled and the number of sixes is obtained and recorded. Using suitable approximations, find the probability of at least 25 sixes in 120 rolls of the die.

Cant use poisson as Mean is 20 as p=1/6 and n=120
Cant use normal as p isnt close to 0.5
p doesn't have to be close to 0.5. It's enough for np >= 5 and n(1-p) >= 5, which are both satisfied in this case, so you can use the normal approximation. See
https://onlinecourses.science.psu.edu/stat414/node/179
3. also your attempt at a poisson approximation yielding a large value of lambda should suggest that a normal approximation should be used as this is the condition for approximating poisson to normal
4. (Original post by HapaxOromenon3)
p doesn't have to be close to 0.5. It's enough for np >= 5 and n(1-p) >= 5, which are both satisfied in this case, so you can use the normal approximation. See
https://onlinecourses.science.psu.edu/stat414/node/179
Ok. The book says p has to be close to 0.5. Are you sure that what you said would work all the time for normal approximations given that its bigger than 5
5. the result for your approximation isn't likely to be very accurate as p isnt close to 0.5 but a normal approximation can be used

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