A balanced die with six sides is rolled 60 times. a. For the binomial distribution of X = number of 6s, what is n and what is p? b. Find the mean and the standard deviation of the distribution of X. Interpret. c. If you observe x = 0, would you be skeptical that the die is balanced? Explain why

a) n = 60, p = 1/6

b) , SD = 2.89

c) I will be skeptical that the die is balanced

Explanation:

a) X = number of 6s

The total number of times the die is rolled is 60, therefore, n = 60

Since the die is balanced, probability that a 6 is obtained,

b1) For a binomial distribution, mean,

Standard Deviation,  

SD = 2.89

c) If observing x = 0 will still mean that the die is balanced, then the mean must have its boundary within 3 standard deviation.

x = 0 is above 3 standard deviations from the mean, if I observe x = 0, I would be skeptical that the die is balanced

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