When can the Empirical Rule be used to identify unusual results in a binomial experiment? Why can the Empirical Rule be used to
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 always be used to identify results in binomial experiments.
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 be used to identify results in binomial experiments when $n p(1-p) \leq 10$.
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 $n p(1-p) \geq 10$.
D. When the binomial distribution is approximately bell shaped, about $95 \%$ of the outcomes will be in the interval from $\mu-2 \mathrm{np}$ to $\mu+2 \mathrm{np}$. The Empirical Rule can be used to identify results in binomial experiments when $\mathrm{np}(1-\mathrm{p}) \geq 10$.

Step 1 ：The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data will fall within three standard deviations of the mean. The rule is so named because 68% of the data falls within one standard deviation, 95% falls within two, and 99.7% falls within three.

Step 2 ：In the context of a binomial experiment, the Empirical Rule can be used to identify unusual results when the binomial distribution is approximately bell shaped. This is because the binomial distribution approaches a normal distribution as the number of trials increases, given that the probability of success remains constant.

Step 3 ：The condition for a binomial distribution to be approximately normal is that both np and n(1-p) are greater than or equal to 10, where n is the number of trials and p is the probability of success. This is because these conditions ensure that the distribution is not too skewed and that there is enough data for the distribution to approximate a normal distribution.

Step 4 ：Therefore, the correct answer is C. When the binomial distribution is approximately bell shaped, about 95% of the outcomes will be in the interval from μ-2σ to μ+2σ. The Empirical Rule can be used to identify results in binomial experiments when np(1-p) ≥ 10.

Step 5 ：Final Answer: \(\boxed{\text{C}}\)