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?

Answer 1

Empirical rule is used to check whether Distribution is Normal or not.

As Empirical rule is used to check whether all the data which is normally Distributed fall within the three standard Deviation along the Mean.

If  68% of the data does not  fall within the first Standard Deviation, 95% of the Data does not fall within the Two Standard Deviation, and 99.7% of the data does not fall within the three Standard Deviation it means the Data is not normally distributed.

Let me Demonstrate this by an example. Consider Mean life span of Rat to be 1.9 years and Standard Deviation of Rat to be .3 months.If we have to calculate whether life of Rat will be more than 0.6 years.

1 St Standard deviation=0.6+0.3 and 1.6+0.3=0.9 to 1.9

2 nd Standard Deviation=0.6 and 1.9+0.3= 0.6 to 2.2 years

Three Standard Deviation=0.6-0.3=0.3 and 2.2+0.3= 0 to 2.5 years

As 95% of the observation will lie above 0.6 years , so remaining 5 % of the data will be distributed in two parts ,i.e one lie above 2.2 years and and another below 0.6 years.

So, Probability of surviving more than 0.6 years = 95% + %$\frac{5}{2}$

                                                                                   =97.5%

 

Answer 2

The empirical rule can be used to identify unusual results in a binomial experiment if the population we take is normally distributed. To check whether the population is normally distributed or not we use empirical rule.

Further Explanation:

Explanation:

The empirical rule is used to check that the given data set is normally distributed. The data values should lie within the three standard deviation of the mean.

Empirical rule is defined as follows,

68% data points will lie within the first standard deviation of the mean.

$\boxed{P\left({\mu-\sigma}\right)=68\%}$

95% data points will lie within the two standard deviation of the mean.

$\boxed{P\left({\mu-2\sigma}\right)=95\%}$

99.7% data points will lie within the three standard deviation of the mean.

$\boxed{P\left({\mu-3\sigma}\right)=99.7\%}$

Here, $\mu$ represents the mean and $\sigma$ represents the standard deviation.

The empirical rule can be used to identify unusual results in a binomial experiment if the population we take is normally distributed. To check whether the population is normally distributed or not we use empirical rule.

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949

2. Learn more about standard normal distribution brainly.com/question/13006989

3. Learn more about confidence interval of mean brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Confidence Interval

Keywords: Z-score, Z-value, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, empirical rule.