SOLUTION: For a binomial probability distribution, it is unusual for the number of successes to be less than μ - 2.5σ or greater than μ + 2.5σ. For a binomial experiment with 10 trials

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Question 1142050: For a binomial probability distribution, it is unusual for the number of successes to be less than μ - 2.5σ or greater than μ + 2.5σ.
For a binomial experiment with 10 trials for which the probability of success on a single trial is 0.2, is it unusual to have more than 5 successes? Compute μ and σ to help you explain why or why not.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Given information:
n+=+10 is the number of trials
p+=+0.2 is the probability of success

First compute the mean mu
mu+=+n%2Ap
mu+=+10%2A0.2
mu+=+2

and the standard deviation sigma
sigma+=+sqrt%28n%2Ap%2A%281-p%29%29
sigma+=+sqrt%2810%2A0.2%2A%281-0.2%29%29
sigma+=+1.26491106406736 (approximate)

Now compute the lower and upper boundaries (L and U)
L+=+mu+-+2.5%2Asigma
L+=+2+-+2.5%2A1.26491106406736
L+=+-1.1622776601684
L+=+-1.16

U+=+mu+%2B+2.5%2Asigma
U+=+2+%2B+2.5%2A1.26491106406736
U+=+5.1622776601684
U+=+5.16

The results we got were: L+=+-1.16 and U+=+5.16

Let x = number of successes

If x > 5, then this is beyond the upper boundary U+=+5.16 since x is a positive whole number.

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Answer: It is unusual to have more than 5 successes.