IQ Test Scores Are Usually

iq Test Scores Are Normally

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of -1.645.

Paper For Above instruction

To find the x-score corresponding to a specific z-score in a normal distribution, we use the z-score formula:

\[ z = \frac{x - \mu}{\sigma} \]

where \(\mu\) is the mean, \(\sigma\) is the standard deviation, and \(x\) is the raw score.

Given: \(\mu = 100\), \(\sigma = 15\), and \(z = -1.645\).

Rearranging for \(x\):

\[ x = z \times \sigma + \mu \]

Plugging in the values:

\[ x = -1.645 \times 15 + 100 \]

\[ x = -24.675 + 100 \]

\[ x \approx 75.33 \]

Therefore, the x-score that corresponds to a z-score of -1.645 is approximately 75.33.

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