Final answer:
To find the percentage of values lying between 115 and 135 in a normal distribution with a mean of 125 and a standard deviation of 10, you would calculate the Z-scores and then consult a Z-table or statistical software. The empirical rule suggests approximately 68% of values would be within one standard deviation of the mean.
Step-by-step explanation:
Calculating the Percent of Values within a Specific Range in a Normal Distribution
When you are given a set of data that is normally distributed, and you want to find the percentage of values that lies between two points, you utilize the properties of the normal distribution.
In the question, you have a normal distribution with a mean of 125 and a standard deviation of 10. To find the percentage of values between 115 and 135, you can use the Empirical Rule or standard normal distribution tables, depending on the exactness required. However, the steps mentioned in the question are assuming the use of a standard normal distribution (Z-score).
Z-scores allow you to determine where a value lies in relation to the mean of the distribution. To convert a raw score to a Z-score, use the formula:
Z = (X - μ) / σ
Where X is the raw score, μ is the mean, and σ is the standard deviation of the distribution.
To find the Z-scores for both 115 and 135:
Z115 = (115 - 125) / 10 = -1
Z135 = (135 - 125) / 10 = 1
At this point, you would consult a Z-table or use statistical software to find the percentage of the distribution within those Z-scores.
Typically, for Z-scores of -1 and 1, you would have approximately 68% of values within that range, according to the Empirical Rule (68-95-99.7 rule). However, the precise percentage would be found using the Z-table, which would give a slightly more accurate result.
Complete Question
Five hundred values are normally distributed with a mean of 125 and a standard deviation of 10.
What percent of the values lies between the interval 115-135?