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Given a binomial random variable with n​ = 100 and p​ = 0.3​, estimate the ​Pr[20...

Given a binomial random variable with n​ = 100 and p​ = 0.3​, estimate the ​Pr[20 ​≤ X​ ≤ 40​]

​Pr[20 ​≤ X​ ≤ 40​] =

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Answer #1

Given: The binomial distribution follows sample size (n) = 100 and the probability of success (p) = 0.3.

The binomial distribution follows the normal distribution when the sample size is greater than 30 and the probability tends to zero.

The mean is calculated as:

The variance is calculated as:

The required probability is calculated as:

Standardizing to standard normal distribution,

Where, the z score is computed from the standard normal table.

The required probability is 0.9708.

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