a fair die is rolled 30 times. find the mean of the probability distribution of the number of 5s obtained for this experiment.
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5/30 should be the probability.
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Answer:
5
Step-by-step explanation:
Let X be the number of 5s obtained in 30 rolls.
Here we have n=30 trials, and the probability of "success" (i.e. getting a 5) in each trial is p=1/6. So X, which counts successes, is binomially distributed:
X ∼ B( 30, 1/6 )
The mean of a binomial distribution B(n,p) is given by np.
Thus, the mean for X's distribution is
np = 30 × 1/6 = 30/6 = 5
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