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In a normal distribution, what percentage of scores lie between the mean 36 and 5 standard deviations above the mean? Use the empirical rule to find your answer.

Sagot :

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