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An Olympic archer is able to hit the bull’s eye 75% of the time. Assume each...

An Olympic archer is able to hit the bull’s eye 75% of the time. Assume each shot is independent of the others. If she shoots 5 arrows, find the standard deviation of the number of bull’s eye she may get. Give your answer to 3 decimal places.

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Answer #1

The appropraite distrbution here is the Binomial distribution because the probability of success, i.e., hiting the bull's eye is given as p=0.75, and also the n=5 independent trials, i.e., when she shoots 5 arrows is given in the question and we are asked to find the standard deviation of the number of bull's eye she may get.

The formula for calculating the standard deviation for the binomial distribution is given by the formula as-

where, n=5, p=0.75

So the standard deviation of the number of bull's eye is calculated as

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