Question

A balanced die with six sides is rolled 60times. X=number of 6s.

If you observe x=0, would you be skeptical that the dice is balanced? Explain why, based on the mean and standard deviation of X.

I already looked for the answers, but there are different opinions and I can't understanding what it is correct. I don't want to know a trivial solution.

60times rolling is pretty large and the binomial distribution will follow the Normal distribution. After calculating the P(X=0)<0.005 , how do I know the dice is balanced or not. And also, the question was "A balanced die with~~" I am confused.

Answer 1

This can be solved using the hypothesis test. As we know that if the die is balanced this would be a case of a binomial distribution and as n is large enough we can use a normal approximation.

Mean = n*p

= 601/6

= 10

Std. Deviation =

=

= 2.887

H0: Probability of each face = 1/6

H1: Atleast one face has a different probabilty than 1/6.

Z = (x-mean)/std. deviation

= (0-10)/2.887

= -3.464

p-value = 0.000532 < 0.05 (significance level) i.e. we can reject H0 and hence we can say that atleast one face a probability different than1/6 and thus it is not a balaced dice.

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