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