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 minus 2 sigmaμ−2σ to mu plus 2 sigmaμ+2σ. the empirical rule can be used to identify results in binomial experiments when np left parenthesis 1 minus p right parenthesis less than or equals 10np(1−p)≤10.

b. when the binomial distribution is approximately bell​ shaped, about​ 95% of the outcomes will be in the interval from mu minus 2 npμ−2np to mu plus 2 npμ+2np. the empirical rule can be used to identify results in binomial experiments when np left parenthesis 1 minus p right parenthesis greater than or equals 10np(1−p)≥10.

c. when the binomial distribution is approximately bell​ shaped, about​ 95% of the outc

Answer 1

The Empirical Rule states that, when the distribution is bell-shaped, around 95% of all observations will be within 2 standard deviations from the mean, which means from μ - 2σ to μ + 2σ.

The binomial distribution is a bell-shaped distribution with:
μ = np and
σ = √(np(1-p))

Therefore, 95% of the outcomes will be in the interval from np-2√(np(1-p)) and np+2√(np(1-p))

Any observation that lies outside this interval (which means greater than np+2√(np(1-p)) or less than np-2√(np(1-p)) ) occurs less then 5% of the times and therefore can be considered "unusual".