A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π = 0.25). to apply the normal distribution to approximate the binomial, what are the mean and standard deviation?

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Mathematics

Violet Bartlett

25 August, 20:35

A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π = 0.25). to apply the normal distribution to approximate the binomial, what are the mean and standard deviation?

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Answers (1)

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Baylee Chen · Answer 1

The expected value or mean of binomial distribution is given by,

E (X) = np = 100*0.25 = 25

probability of failure = 1-0.25=0.75

Variance[V (X) ] = npq = 100*0.25*0.75 = 18.75

Standard deviation = √V (X) = √18.75 = 4.33