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

Question

Mathematics

Jan Patel

31 December, 15:18

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

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Answers (1)

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Luna Arias · 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".