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curukksm

Answered question

2022-09-09

The normal distribution is a good estimate for which of the binomial distributions. n=40, p=0.1

Answer & Explanation

Nelson Santana

Beginner2022-09-10Added 13 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 n 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=40, p=0.1 therefore q=0.3, so we have,
np=40*0.1=4<5

n q = 40 * 0.9 = 36 \geq 5

So, we can conclude that the normal distribution is not good estimate for binomial distribution in our case.

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