Question

Using the empirical rule, in a normal distribution what percentage of values would fall into an interval of 29.96 to 184.04 where the mean is 107 and standard deviation is 38.52?

Answer 1

Approximately 95% of values in a normal distribution with a mean of 107 and a standard deviation of 38.52 would fall within the interval of 29.96 to 184.04, as per the empirical rule.

Step-by-step explanation:

Using the empirical rule, also known as the 68-95-99.7 rule, we can determine what percentage of values would fall within a certain range for a normal distribution. The given distribution has a mean (μ) of 107 and a standard deviation (σ) of 38.52. According to the empirical rule, approximately 95% of the values fall within two standard deviations of the mean. This can be calculated by adding and subtracting two standard deviations from the mean (μ ± 2σ).

In this case, the range would be from 107 - 2(38.52) to 107 + 2(38.52), which is from 29.96 to 184.04. Therefore, we would expect approximately 95 percent of the values to fall between 29.96 and 184.04 in a normal distribution with the given mean and standard deviation.