Answer :
Final answer:
Using the 68-95-99.7 rule in normal distribution, about 49.85% of the values from the distribution lie between 13 and 25.
Explanation:
In statistics, the 68-95-99.7 rule is often referred to when dealing with a normal distribution. It it also known as the empirical rule or the three-sigma rule where approximately 68% of values lie within one standard deviation from the mean, 95% within two standard deviations, and 99.7% lie within three standard deviations.
Given that you are looking for the percentage of values between 13 and 25 in a distribution with a mean of 13 and standard deviation of 4, first we need to calculate how many standard deviations 25 is from the mean (13). This is done by subtracting the mean from 25 and dividing by the standard deviation: (25 - 13)/4 = 3.
Therefore, 25 is three standard deviations more than the mean of 13. So, if we apply the 68-95-99.7 rule, since 13 is the mean and 25 lies within 3 standard deviations, about 99.7% of the data lies between 13 and 25. However, since we are only looking into the side of the distribution from the mean (13) to 25, we should take half of 99.7%, which is 49.85%. So approximately 49.85% of the data in this distribution falls between 13 and 25.
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