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A distribution of scores has a mean of ?=100 and a standard deviation of ?=10. For...

A distribution of scores has a mean of ?=100 and a standard deviation of ?=10. For an x value of 140, calculate the corresponding z-score.Can you also interpret what the z-score of x means (x=140)?

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Answer #1

For the distribution with a mean of ?=100 and a standard deviation of ?=10.

The Z score is calculated as:

The Z score for a normal distribution is the no of standard deviations the X is far from the mean. If the Z score is negative then the X value is -Z nos Standard deviation below the mean and if it is positive then the value X is Z no of standard deviations above the mean.

Since here Z=4 then we can say that the variable X is 4 standard deviation above the mean.

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