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VaneB
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Homework Statement
The scores on an exam are normally distributed, with a mean of 77 and a standard deviation of 5. What percent of the scores are greater than 87?
Standard deviation is a measure of how spread out a set of data is from its mean or average. It tells us how much the data values deviate from the mean.
To calculate the standard deviation, we first find the mean of the data set. Then, for each value, we find the difference between that value and the mean. We square each difference, add them together, divide by the total number of values, and then take the square root of that result.
Standard deviation is important because it allows us to understand the variability or spread of a data set. It is used to compare different data sets and to make inferences about the population from a sample.
Standard deviation and variance are both measures of variability in a data set. However, variance is the average of the squared differences from the mean, while standard deviation is the square root of the variance. Standard deviation is more commonly used because it is in the same units as the original data.
Percent of scores is related to standard deviation because it tells us how many data values fall within a certain number of standard deviations from the mean. For example, about 68% of the data values will fall within one standard deviation from the mean, and about 95% will fall within two standard deviations from the mean.