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If an IQ test has an average of 100 and a standard deviation of 15, what raw score do 2.5% of people score below?

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Final answer:

To find the raw score that 2.5% of people score below on an IQ test with an average of 100 and a standard deviation of 15, you would use the z-score for 2.5% from a standard normal distribution which is -1.96. Using the raw score formula, the score is calculated as approximately 70.6.

Step-by-step explanation:

If an IQ test has an average of 100 and a standard deviation of 15, the raw score that 2.5% of people score below can be found by looking at a standard normal distribution table or using a statistical software that can provide the z-score corresponding to the cumulative probability of 0.025 (2.5%). From a z-table, the z-score that corresponds to 2.5% is approximately -1.96. This value is the number of standard deviations from the mean. To find the raw score, you use the formula:

Raw Score = Mean + (Z-score × Standard Deviation)

Substituting the respective values into the formula:

Raw Score = 100 + (-1.96 × 15)

Raw Score = 100 - 29.4

Raw Score = 70.6

So, 2.5% of people score below 70.6 on this IQ test.

User Truly
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