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A normal distribution has mean =μ62 and standard deviation =σ20. Find and interpret the z-score for =x53.The z-score for =x53 is . So 53 is standard deviations ▼above the mean =μ62.

Question

A normal distribution has mean =μ62 and standard deviation =σ20. Find and interpret the z-score for =x53.The z-score for =x53 is . So 53 is standard deviations ▼above the mean =μ62.

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Solution

To calculate the z-score, we use the formula:

z = (X - μ) / σ

where: X is the score from the dataset, μ is the mean, and σ is the standard deviation.

Given that X = 53, μ = 62, and σ = 20, we substitute these values into the formula:

z = (53 - 62) / 20 = -0.45

The z-score is -0.45. This means that the score of 53 is 0.45 standard deviations below the mean of 62. In other words, 53 is slightly less than the average score.

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