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yamyekay3

Answered question

2022-09-11

The normal distribution is a good estimate for which of the binomial distributions. n=200, p=0.08

Answer & Explanation

Duncan Kaufman

Beginner2022-09-12Added 17 answers

The probability of k success in nn attempts using the Binomial Distribution calculate using the formula,

P (n = k) = C (n, k) p^{k} q^{n - k}

where is p probabilty, q=1−p and nn sample size
To compute some binomial probabilities, can be tedious and subject to mistakes. Fortunately, the normal curve can often be used to obtain a satisfactory estimate of a binomial probability. The normal distribution provides a good estimate of the binomial distribution when,

n p \geq 5

n q \geq 5

where is p probabilty, q=1−p and n sample size.
Since n=200, p=0.08 therefore q=0.92, so we have,

n p = 200 * 0.08 = 16 \geq 5

n q = 200 * 0.92 = 184 \geq 5

So, we can conclude that the normal distribution is good estimate for binomial distribution.

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