When can the Empirical Rule be used to identify unusual results in a binomial ex

Question

When can the Empirical Rule be used to identify unusual results in a binomial experiment? Why can the Empirical Rule be used to identify results in a binomial experiment? Choose the correct answer below. A. When the binomial distribution is approximately bell shaped, about 95% of the outcomes will be in the interval from mu - 2 sigma to mu + 2 sigma. The Empirical Rule can be used to identify results in binomial experiments when np(1 - p) greaterthanorequalto 10. B. When the binomial distribution is approximately bell shaped, about 95% of the outcomes will be in the interval from mu- 2 sigma to mu +2 sigma. The Empirical Rule can always be used to identify results in binomial experiments. C. When the binomial distribution is approximately bell shaped, about 95% of the outcomes will be in the interval from mu- 2 sigma to mu +2 sigma. The Empirical Rule can be used to identify results in binomial experiments when np(1 - p) lessthanorequalto 10. D. When the binomial distribution is approximately bell shaped, about 95% of the outcomes will be in the interval from mu - 2np to mu + 2np. The Empirical Rule can be used to identify results in binomial experiments when np(1 - p) greaterthanorequalto 10.

Explanation / Answer

Answer A)

Empirical Rule : This rule gives the approximate % of observations within 1 standard deviations (68%), 2 standard deviations (95%) and 3 standard deviations (99.7%) of the mean when the histogram is well approximated by a normal curve.

Also, we need np>= 10 and n(1-p) >= 10 in order for the normal approximation to be reasonable.

Hence,

When the binomial distribution is approximately bell shaped, about 95% of the outcomes will be in the interval from µ-2 and µ+2. The Empirical Rule can be used to identify results in binomial experiments when np(1-p)>=10.

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