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Sampling Statistics question

An unbiased dice is thrown 70 times.
Find the probability that the total score exceeds 260.

T represents the total score of the 70 dice
X represents the mean of the sample. I calculated that X~N(3.5, 1/24)
P(T>260)=P(V>260.5) where V is the appropriate normal distribution.
So, this equals P(X>260.5/70)=P(X>260+1/140)
Let Z=(X-3.5)/sqrt(1/24). So Z~N(0,1)
So P(X>260.5/70)=P(Z>(260.5/70-3.5)/sqrt(1/24))=P(Z>1.085) (to 3 s.f)
using tables this is 1-0.8611=0.1389.
However this is not the answer in my textbook. Can anybody spot a mistake?
Thanks
Original post by MEPS1996
An unbiased dice is thrown 70 times.
Find the probability that the total score exceeds 260.

T represents the total score of the 70 dice
X represents the mean of the sample. I calculated that X~N(3.5, 1/24)
P(T>260)=P(V>260.5) where V is the appropriate normal distribution.
So, this equals P(X>260.5/70)=P(X>260+1/140)
Let Z=(X-3.5)/sqrt(1/24). So Z~N(0,1)
So P(X>260.5/70)=P(Z>(260.5/70-3.5)/sqrt(1/24))=P(Z>1.085) (to 3 s.f)
using tables this is 1-0.8611=0.1389.
However this is not the answer in my textbook. Can anybody spot a mistake?
Thanks


I can see nothing wrong. I have done the question slightly differently, by considering the total score on the 70 dice and got exactly the same answer as you. AS a matter of interest, what answer did the text book give? It is not impossible for it to be wrong.

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