Question

In: Statistics and Probability

17#13 Suppose we roll a fair six-sided die and sum the values obtained on each roll,...

17#13

Suppose we roll a fair six-sided die and sum the values obtained on each roll, stopping once our sum exceeds 289. Approximate the probability that at least 76 rolls are needed to get this sum.

Expert Solution

Answer: 0.96604

Explanation:

In an experiment of rolling of a six-sided fair die, the random variable X denoting sum of the outcomes in the single roll, has following parameters:

Mean,

Standard deviation,

Then the probability that at least 76 are needed to get 289 is one minus the probability that 75 are not enough. If Y is the sum of the 75, this is

will have the following parameters:

Mean,

Standard deviation, .

Now, we calculate the probability that the sum of 75 rolls is lower than 289.5, i.e. P(Y<289.5)

R-output

So, there is a 0.96604 probability that at least 76 rolls are needed to get the sum of 289.

orchestra answered 1 year ago

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