Answer :
Answer:
Step-by-step explanation:
Certainly! Let’s use the empirical rule to find the percentage of scores between the mean and 5 standard deviations above the mean in a normal distribution.
Empirical Rule:
The empirical rule, also known as the 68-95-99.7 rule, provides a quick estimate of where most values lie in a normal distribution:
Approximately 68% of values fall within 1 standard deviation from the mean.
About 95% of values fall within 2 standard deviations from the mean.
Roughly 99.7% of values fall within 3 standard deviations from the mean123.
Given Information:
Mean (μ) = 36
Standard deviation (σ) = 5
Calculations:
To find the value 5 standard deviations above the mean, we can calculate:
Upper limit = μ+5σ=36+5⋅5=61
Percentage of Scores:
We want to find the percentage of scores between the mean (36) and the upper limit (61).
Since 61 is 5 standard deviations above the mean, we can use the empirical rule:
Approximately 95% of scores lie between 36 and 61 (within 2 standard deviations above the mean).
Therefore, approximately 95% of scores fall between the mean (36) and 5 standard deviations above the mean (61) in this normal distribution
