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Suppose X∼N(12.5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable.\

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Answer:

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Step-by-step explanation:

Using the normal distribution, it is found that x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.

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In a normal distribution with mean  and standard deviation , the z-score of a measure X is given by:

The z-score measures how many standard deviations the measure X is from the mean, above or below.  

X∼N(6.5,1.5), which means that .

The measure is

The z-score is:

The measure x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.

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