Answer :

Final answer:

To find the location of an X value on a distribution curve, we have to calculate the z-score. Given X = 31.3, the mean (μ) as 35.8, and the standard deviation (σ) as 1.6, the X value will be located to the left of the mean on the curve as its z-score will be a negative.

Explanation:

The question asks us to find where the given X value would be on the curve, given the mean (μ) and the standard deviation (σ). It's important to understand that a mean is the average of a data set and the standard deviation is a measure of the amount of variation or dispersion of a set of values. The given X value (31.3) is less than the mean (35.8), which means it will be located to the left of the mean on the curve.

To accurately locate it, we should convert it into a z-score by using the formula z = (X - μ) / σ. Here, X = 31.3, μ = 35.8, and σ =1.6. Plugging these values in, we get a z-score which gives us the number of standard deviations away from the mean our X value is located.

Small negative z-scores mean the X value lies to the left and near to the mean, large negative z-scores indicate that the X value lies far to the left of the mean. Conversely, positive z-scores represent X values to the right of the mean. So using these concepts, we can visualize where the X value is located.

Learn more about Standard Normal Distribution here:

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