The scores on a standardized test are normally distributed with a mean of 90 and standard deviation of 8. What test score is 4 standard deviations below the mean?

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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**Question:**

The scores on a standardized test are normally distributed with a mean of 90 and a standard deviation of 8. What test score is 4 standard deviations below the mean?

**Explanation:**

To find the test score that is 4 standard deviations below the mean, you can use the formula:

Score = Mean - (Standard Deviation × Number of Standard Deviations Below)

Given:
- Mean = 90
- Standard Deviation = 8
- Number of Standard Deviations Below = 4

Calculation:
Score = 90 - (8 × 4) = 90 - 32 = 58

Therefore, the test score that is 4 standard deviations below the mean is 58.
Transcribed Image Text:**Question:** The scores on a standardized test are normally distributed with a mean of 90 and a standard deviation of 8. What test score is 4 standard deviations below the mean? **Explanation:** To find the test score that is 4 standard deviations below the mean, you can use the formula: Score = Mean - (Standard Deviation × Number of Standard Deviations Below) Given: - Mean = 90 - Standard Deviation = 8 - Number of Standard Deviations Below = 4 Calculation: Score = 90 - (8 × 4) = 90 - 32 = 58 Therefore, the test score that is 4 standard deviations below the mean is 58.
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