2 outcomes: Archer shoots an arrow into the target 1000 times....

Nzzska

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Apr 1, 2017
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Hey,
first time using this forum and I have this problem Im struggling to solve(Sorry english is not my native language :p).

Archer shoots an arrow into the target 1000 times. The probability of arrow hitting the target is 3/4 (0.75).
What is probability of arrow hitting target any number between 650 and 750 times ?

My initial thought was using bernoulli's trials to figure out seperate probabilities of k={650,651...750}, however, I cant figure out the way how to add them efficiently. Or maybe there is better way of looking at this problem?
 
Hey,
first time using this forum and I have this problem Im struggling to solve(Sorry english is not my native language :p).

Archer shoots an arrow into the target 1000 times. The probability of arrow hitting the target is 3/4 (0.75).
What is probability of arrow hitting target any number between 650 and 750 times ?

My initial thought was using bernoulli's trials to figure out seperate probabilities of k={650,651...750}, however, I cant figure out the way how to add them efficiently. Or maybe there is better way of looking at this problem?

Since n is "large" you could use a normal approximation to the binomial where mu = np and sigma = sqrt(npq).
Then find P(649.5<X<750.5) assuming inclusivity.
 
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